TLDR:

The perception of MC (male circumcision) and FGC (female genital cutting) in the West are skewed by familiarity with MC (particularly in the US), and unfamiliarity with FGC which is viewed as a barbaric "mutilating" practice practised by "outsiders" and "savages" in Africa. The common conception of FGC as a mutilating procedure done to restrict female sexuality drives the separation of these two practices in public discourse. Because MC is a familiar practice in the US it is seen as benign and even beneficial to health. The US takes a similar view on both female genital cosmetic surgeries (FGCS) and intersex normalisation surgeries, which are both viewed as enhancements and beneficial, despite distinct anatomical parallels to forms of FGC [1,9,10]. The key feature seems to be how familiar or foreign such a bodily modification is - throughout history people have viewed their own bodily modifications as benign and beneficial and those of outsiders as barbaric and mutilating. See - Chinese foot binding, MC, FGC, corsetting, ritual scarification etc.

An additive effect to this was that FGC become linked to patriarchy in the 1970s due to the influence of the Hosken report. This report has since been largely repudiated. Despite significant criticism from experts in the field, the UN/WHO have entrenched this division, and the mainstream opinion remains that MC and FGC are incomparable. On this basis US law (unsurprisingly) treats the familiar MC as a "benign" and "harmless" practice, whilst treating any and all forms of FGC (including forms less invasive than MC) as utterly impermissible.

Western perceptions of female genital cutting (FGC) and male circumcision (MC) are not rooted in well-established empirical evidence as surveyed by a team of leading researchers in FGC [1]. The common view relies on poorly substantiated tropes. The perception of FGC as sexually crippling and leading to poor health outcomes is not well substantiated by the best evidence [1]. Similarly the motivations for FGC are varied, and with a few exceptions, FGC is not well explained by patriarchy.

Put bluntly - there is a double standard in how FGC practices in Africa are treated versus FGCS, MC and intersex surgeries. A wide ranging body of scholars has stated this clearly- see [7]. This hypocritical attitude is not based on a solid empirical understanding of the effects and motivations of FGC practices in Africa, and neither does it critically examine the evidence and motivations for MC within the US. Attitudes towards FGC are based on an "orientalizing" approach [8] towards outsider cultures and the global enforcement of FGM band reflects the far greater power of the global North vs the global South.

On the case of more minor forms of FGC, there are signs that the "firewall" between FGC and MC is breaking down. The trial of Dr Jumala Nagarwala in 2017 was over a religiously mandated form of FGC, the "ritual nick", which on any account was less invasive than MC. This particular trial was ended on a technicality, but the issue remains open - forms of FGC less invasive than MC are deemed impermissible. This seems untenable. In the US it seems likely that some more "minor" forms of FGC will become permissible. In countries with a much lower prevalence of MC (particular Scandinavian countries), it seems likely that the censure applied to even "minor" forms of FGC will be applied to MC . This may not take the form of outright prohibition - the laws in Sweden on MC permit it, but regulate it tightly.

Academic opinion is solidifying into two camps - one which considers any modification of children's genitalia (barring medical necessity) to be impermissible (see [7]), and one which has already advocated for minor forms of FGC to be permitted (see Arora & Jacobs; the Seattle Compromise; 2016 Economist article - "FGM: An agonising choice"). It seems likely that this debate will become mainstream within the next decade or two, as awareness increases of the prevalence of minor forms of FGC, and cases analogous to Dr Nagarwala appear again.

Main body:

In my answer I will refer to “female genital cutting” (FGC), instead of FGM. For reasons why, refer to [2]. Suffice to say – Many women who have had their genitalia cut largely do not feel “mutilated”, and feel this is a value-laden term which they would rather not have applied to their bodies, and it leads to stigma and shame. I choose to respect these women’s wishes, given their voice is not often heard. Furthermore, this term does actual, active harm to women who have been cut (again refer to [2]).

A source I will repeatedly refer to throughout this answer is a Hastings Centre report entitled "Seven things to know about female genital surgeries in Africa". I provide a non-paywalled link to this report below. This report was authored by 15 international experts in FGC, including a number of gynaecologists who run clinics for women with FGC, alongside a number of anthropologists, legal experts and feminists. It includes both advocates for liberalisation of laws around FGC, and also a large number of gynaecologists who run clinics for women with FGC who are concerned about the effect that sensationalism has on the sexual health of women in their clinic. It also has anthropologists who are well qualified to speak on the motivations for FGC. It is worth noting that a number of these authors are also authors of [7] and can hardly be described as "FGM apologists" - however, they call for greater balance in the debate, as they believe the current debate is likely to be un-productive in abolishing FGC in the long-run. I'll start my answer by quoting the abstract of the report:

"Western media coverage of female genital modifications in Africa has been hyperbolic and onesided, presenting them uniformly as mutilation and ignoring the cultural complexities that underlie these practices. Even if we ultimately decide that female genital modifications should be abandoned, the debate around them should be grounded in a better account of the facts."

The common Western perception of FGC was shaped predominantly in the 1970s when awareness of FGC was just becoming mainstream. At that time the data available was of poor quality and restricted to Sudan & Somalia, where the most extreme form of FGC (infibulation) is performed with the intention of oppressing female sexuality, routed in a (highly problematic) Islamic Purdah ideology. At the same time in 1970s feminism there was a desire to create a "global sisterhood". Fran Hosken believed that FGC/M was irrevocable proof of a global patriarchy intent on oppressing female sexuality and suggested that this was rock solid evidence for the need for a "global sisterhood". To this end the highly influential Hosken report was authored. At the time anthropologists pointed out that gender roles are known to vary substantially across cultures and that a "global sisterhood" based on a common female experience was likely to be flawed.

This paradigm has stuck, despite the past 3 decades of critical scholarship in anthropology and medicine largely refuting the Hosken reports findings. FGC has been found to be a far more widespread practice than initially thought, with many cultural groupings in Africa, the Middle East, and SE Asia practising some form of FGC.

The Western view of FGC as a mutilating practice which removes any capacity for sexual pleasure and causes drastic health outcomes is unfounded.

The Hastings Report finds that:

"Research by gynecologists and others has demonstrated that a high percentage of women who have had genital surgery have rich sexual lives, including desire, arousal, orgasm, and satisfaction, and their frequency of sexual activity is not reduced"

This may be a surprising claim. This claim was based on research by Lucrezia Catania and Jasmine Abdulcadir (both authors of the Hastings report). In their original paper they conclude: (emphasis mine)

“embryology, anatomy, and physiology of female erectile organs are neglected in specialist textbooks. In infibulated women, some erectile structures fundamental for orgasm have not been excised. Cultural influence can change the perception of pleasure, as well as social acceptance. Every woman has the right to have sexual health and to feel sexual pleasure for full psychophysical well-being of the person. In accordance with other research, the present study reports that FGM/C women can also have the possibility of reaching an orgasm. Therefore, FGM/C women with sexual dysfunctions can and must be cured; they have the right to have an appropriate sexual therapy.”

The aim of these gynaecologists is to treat women with FGC and sexual dysfunction. These women will have had their sexual dysfunctions dimissed on the basis of their FGC - I have the greatest respect of Catania and Abdulcadir who advocate for the rights of their patients to receive proper treatment. All too often women with FGC are not seen as humans, but instead as their genitals - a point remarked upon by Fuambai Sia Ahmadu elsewhere.

This is indeed a surprising result, given that the external clitoris is heavily innervated, and many women enjoy and reach orgasm from stimulation of the external clitoris. Human sexuality is a highly complicated field, and direct "one-to-one" mappings of nerve endings to sexual satisfaction do not have much value. The anthropologist Sara Johnsdotter addresses this in [3], in reply to discussion of how circumcision (which removes the highly innervated foreskin) affects sexual functioning and satisfaction. Sara Johnsdotter sums up the situation [3]:

"Most women who have been circumcised seem to have gratifying sexual lives. Some women testify that circumcision had negative effects on their sexual well-being, and some opt for reconstructive genital surgery. Most men who have been circumcised seem to have gratifying sexual lives. Some men testify that circumcision had negative effects on their sexual well-being, and some opt for reconstructive genital surgery."

Despite the complexities of how genital cutting affects sexual satisfaction, it is a logical necessity that sexual sensation is changed/reduced - both the removal of the highly innervated clitoral glans (female) and the foreskin (male) clearly oblate any sensation which is experienced in the removed tissues. Given that non-consenting children cannot choose whether they would have this tissue removed, a body of bioethicists, clinicians, anthropologists, and legal experts suggest that both MC and FGC should be seen as impermissible [7].

Johnsdotter gives some explanation as to why the attenuation of sexual sensation apparently has (in many/most cases) a relatively marginal effect on sexual satisfaction:

"[...] Social and cultural dimensions are integral to lived sexuality. Findings from the emergent research field of the ‘anthropology of sensations’ demonstrate how sensations are culturally learned – to grow up in a certain society entails learning to ‘read’ one’s body in specific ways: ‘Sensory meaning is never a question of physiology; it is always mediated by culture, in the sense of the ways of life, language, ritual practices, beliefs and aesthetics of a group, community, or society’ (Hinton et al. 2008). Sensation schemas will impact how we perceive bodily signals, whether we notice them at all, and what kind of meanings we ascribe to them. This is also true for sexual activities: we need to ‘decode’ bodily sensations and relate them to culturally and socially created erotic meanings in order to experience sexual pleasure (Cameron and Kulick 2003; Tiefer 2004). [...] the current academic focus on the role of genitalia in understanding sexual pleasure is a dead end. While genitalia usually are central to sexual activity, and can be seen as a prerequisite for sexual intercourse, it is a misapprehension to see the state of them (cut or uncut) as determinative of the individual’s experience of the sexual encounter. "

It is broadly not the case, as it commonly is assumed, that women with FGC are physiologically incapable of orgasm due to the removed of sensitive tissues, and indeed in most cultures which practice FGC this is not the intention either (see above comments from [1]). These assumptions prove harmful to women with FGC who live in the West (see [1] and [2]). Nevertheless, in both cases sensitive tissues are removed, and to many (including the author) this is ethically problematic [7]. Nevertheless - before we reach the conclusion that FGC is impermissible, we must base our arguments on what the evidence actually says, not what we might wish it to say. The best quality evidence does not support the "hyperbolic and onesided" claims of the sexual/health effects of FGC. This does not necessarily obviate the impermissiblity of FGC, if it is recognised that children have a right to bodily integrity/autonomy, and it simply is a wrong to cut any part of a child's body (let alone their genitalia) without medical necessity.

And on the topic of health outcomes:

"The widely publicized and sensationalized reproductive health and medical complications associated with female genital surgeries in Africa are infrequent events and represent the exception rather than the rule."

Claims about the motivations of FGC being the patriarchal oppression of women are unfounded:

“The empirical association between patriarchy and genital surgeries is not well established. The vast majority of the world’s societies can be described as patriarchal, and most either do not modify the genitals of either sex or modify the genitals of males only. There are almost no patriarchal societies with customary genital surgeries for females only. Across human societies there is a broad range of cultural attitudes concerning female sexuality—from societies that press for temperance, restraint, and the control of sexuality to those that are more permissive and encouraging of sexual adventures and experimentation—but these differences do not correlate strongly with the presence or absence of female genital surgeries.”

Bear in mind that:

"In almost all societies where there are customary female genital surgeries, there are also customary male genital surgeries, at similar ages and for parallel reasons. In other words, there are few societies in the world, if any, in which female but not male genital surgeries are customary. As a broad generalization, it seems fair to say that societies for whom genital surgeries are normal and routine are not singling out females as targets of punishment,sexual deprivation, or humiliation. The frequency with which overheated, rhetorically loaded, and inappropriate analogies are invoked in the antimutilation literature (“female castration,” “sexual blinding of women,” and so on) is both a measure of the need for more balanced critical thinking and open debate about this topic and one of the reasons we are publishing this public policy advisory statement."

Whilst clearly in Sudan/Somalia/Djibouti the intention is to oppress women's sexuality, this is not a good explanation for all FGC, but is instead a facet of those particular cultures:

"In some societies where genital surgeries are customary for females and males ... chastity and virginity are highly valued, and ... infibulation may be expressive of these values, but those chastity and virginity concerns are neither distinctive nor characteristic of all societies for whom genital surgeries are customary. Indeed, female genital surgeries are not customary in the vast majority of the world’s most sexually restrictive societies."

Of particular note is that "female genital surgery should not be blamed on men or on patriarchy":

"Demographic and health survey data reveal that when compared with men, an equal or higher proportion of women favor the continuation of female genital surgeries. "

FGC is performed for many reasons. In the Kono tribe in Sierra Leone FGC is part of the female initiation ceremony, Bondo. In Sierra Leone [8]:

"there is no cultural obsession with feminine chastity, virginity, or women’s sexual fidelity, perhaps because the role of the biological father is considered marginal and peripheral to the central ‘matricentric unit.’ … Kono culture promulgates a dual-sex ideology … [The] power of Bundu, the women’s secret sodality [i.e., initiation society that manages FGC ceremonies], suggest positive links between excision, women’s religious ideology, their power in domestic relations, and their high profile in the ‘public arena."

FGC is performed generally in a parallel initiation rite to a male cutting ritual. A common reason given is that the fleshy foreskin is a female element in a male and must be cut away to attain full manhood, and the external part of the clitoris is a phallic and male element and must be cut away to attain full womanhood. From the Hastings Report:

"From the perspective of those who value these surgeries, they are associated with a positive aesthetic ideal aimed at making the genitals more attractive—“smooth and clean.” The surgeries also serve to enhance gender identity from the point of view of many insiders. "

Despite substantial criticism of the UN/WHO position on FGC there has been little engagement with dissenting expert opinions. Many of these experts believe that the current discourse around FGC is harmful to women with FGC and is likely to be unproductive in reducing the prevalence of FGC. The UN/WHO position on FGC is largely determined by activists and mainstream rhetoric, and not by experts in the field (see [1], [2]). This should be contrasted with the usual expert-led approach of the WHO in other areas. There exist clear parallels and similarities with MC (at least MC performed under similar conditions to the FGC), despite the mainstream opinion in the West being that these are two separate discussions. In the words of Zachary Androus:

“The fact of the matter is that what’s done to some girls [in some cultures] is worse than what’s done to some boys, and what’s done to some boys [in some cultures] is worse than what’s done to some girls. By collapsing all of the many different types of procedures performed into a single set for each sex, categories are created that do not accurately describe any situation that actually occurs anywhere in the world.”

The paradigm that MC and FGC are two incomparable practices is also due to the fact that MC has been common in many Western nations, being introduced as a mainstream practice in the 1900s in the anglosphere - UK, USA, NZ, AUS. In the US (the main driver of the WHO FGM policy) MC is still routine. Hence this familiar practice is seen as relatively benign, "something which has always been done", whereas the foreign practice of FGC (in any form, even comparably minor forms) is seen as "backward", "barbaric" and "savage". This was remarked upon by the renowned anti-FGM activist Hanny Lightfoot-Klein:

“… the mainstream anti-FGC position is premised upon an orientalizing construction of FGC societies as primitive, patriarchal, and barbaric, and of female circumcision as a harmful, unnecessary cultural practice based on patriarchal gender norms and ritualistic beliefs. … Lambasting African societies and practices (while failing to critique similar practices in the United States) … essentially implies that North American understandings of the body are “scientific” (i.e., rational, civilized, and based on universally acknowledged expertise), while African understandings are “cultural” (i.e., superstitious, un-civilized, and based on false, socially constructed beliefs). [Yet] neither of these depictions is accurate. North American medicine is not free of cultural influence, and FGC practices are not bound by culture—at least not in the uniform way imagined by opponents.”

The WHO/UN adopts a "zero-tolerance" stance towards FGC in any form (the author believes this to be the correct path to take, but would suggest the key moral argument - bodily integrity/autonomy - should be applied to all children, see [7]). This includes even the "ritual nick" or similar minor forms as practised widely across SE Asia, in the Muslim populations within Malaysia, Indonesia and Singapore. In total it is estimated that around 60-70 million women have had one of these "minor" forms of FGC performed on them. This point has particular relevance to the US, which I will address next.

In 2017 Dr Jumala Nagarwala was put on trial in Detroit, Michigan under the FGM law. Dr Nagarwala is part of an Islamic sect, the Dawoodi Bohra. In the Dawoodi Bohra both boys and girls are "circumcised" to mark their presence in the Abrahamic covenenant. The cutting for girls consists of a ritual nick with no removal of flesh, whereas for boys it entails removal of the foreskin. The defence emphasized the "low risk" nature of the practice and drew parallels to MC. In this case MC would be on any account a considerably more invasive procedure. The judge ruled that the Federal FGM law was dismissed as being unconstitutional, as there are restrictions on what laws can be at the Federal vs the State level, this has in effect just displaced the problem to the State courts. If a repeat of this trial were to come, the defence would make (a very good) case that if MC is allowed for religious reasons, then so too should this "minor" form of FGC. The likely outcome of this in the US is that this kind of "minor" FGC would be allowed, under the idea of "non-discrimination" - the law cannot be one thing for males, and another for females, there has to be some sort of logical consistency. Above answers have failed to take into account that this is the only instance where US law has been brought to bear on FGM. I am not sure why this has be omitted from consideration, and perhaps other answerers would like to take this into account in their answers.

To address some points made in other answers on health effects: In response to the promotion of male circumcision in America, a number of health professionals across Northern Europe published a response, stating they believe the American view is seriously biased [9]:

"Seen from the outside, cultural bias reflecting the normality of nontherapeutic male circumcision in the United States seems obvious,[…] the report’s conclusions are different from those reached[ …] in other parts of the Western world, including Europe, Canada, and Australia. […], only 1 of the arguments put forward by the American Academy of Pediatrics has some theoretical […]; namely, the possible protection against urinary tract infections in infant boys, which can easily be treated with antibiotics without tissue loss. The other claimed health benefits, including protection against HIV/AIDS, genital herpes, genital warts, and penile cancer, are questionable, weak, and likely to have little public health relevance in a Western context, and they do not represent compelling reasons for surgery before boys are old enough to decide for themselves[...] The most important criteria for the justification of medical procedures are necessity, cost-effectiveness, subsidiarity, proportionality, and consent. For preventive medical procedures, this means that the procedure must effectively lead to the prevention of a serious medical problem, that there is no less intrusive means of reaching the same goal, and that the risks of the procedure are proportional to the intended benefit. In addition, when performed in childhood, it needs to be clearly demonstrated that it is essential to perform the procedure before an age at which the individual can make a decision about the procedure for him or herself.”

Some comments to clear up any possible misconceptions about my stance on the acceptability of non-therapeutic genital alterations of children - I am against any cutting of a child's genitals, barring medical necessity. For further detail on this view see [7]. Briefly - the ethical arguments proposed for why FGC is wrong, also apply to male circumcision and intersex normalisation surgeries. If we are to declare bodily autonomy and integrity as human rights, they apply to all humans - male, female and intersex. And if we wish to judge other cultures, we should check that our culture is consistent with the measure we use.

However - the current discourse around FGC is stigmatising and harmful to women with FGC in the West who grow up with the expectation that their sex lives will be painful and unsatisfactory, potentially encouraging a "catastrophising" response [2]. Moreover it is not clear whether the overly sensationalised rhetoric used is effective in combating FGC - the cultures which practice FGC are fully aware of the effects of it on sexuality/health outcomes and "scare stories" are unlikely to be effective, as they can be readily dismissed. The best approaches to tackling FGC are local solutions - activists/dissenters within the practising communities being supported and encouraging non-cutting initiation rites. It is also important to note that the actual needs of these women may well be different to what we assume. For many of these women access to clean drinking water, education for themselves and their children, economic freedom and a peaceful (non civil-warring) country are priorities above FGC. Sara Johnsdotter has explored the various social tensions underpinning FGC and finds that it is usually abandoned on migration to the West, on which social dynamics change dramatically. It seems likely that increasing access to education & economic freedom will lead to abandonment of FGC almost as a "side-effect".

The main citation for the (likely controversial claims on FGC) can be found here: (this is citation 1 - “Seven Things to Know about Female Genital Surgeries in Africa.” Hastings Center Report)

https://www.sfog.se/media/295486/omskarelse_rapport.pdf

Finally I should thank a number of contributors who have made helpful comments on how to improve this answer - Russel McMahon, Ted Wrigley and Andrew Grimm. I think the general feeling was that my answer was too long and made use of "intimidation by citation" instead of quoting relevant parts of my sources.

Citations:

[1] “Seven Things to Know about Female Genital Surgeries in Africa.” Hastings Center Report. Can be found at: https://www.sfog.se/media/295486/omskarelse_rapport.pdf

[2] Earp, Brian D. “Protecting Children from Medically Unnecessary Genital Cutting Without Stigmatizing Women’s Bodies: Implications for Sexual Pleasure and Pain.” Archives of Sexual Behavior, 2020, doi:10.1007/s10508-020-01633-x.

[3] Johnsdotter, Sara. “Discourses on Sexual Pleasure after Genital Modifications: the Fallacy of Genital Determinism (a Response to J. Steven Svoboda).” Circumcision, Public Health, Genital Autonomy and Cultural Rights, May 2017, pp. 46–55., doi:10.4324/9781315095684-6.

[4] Rashid, Abdul, and Yufu Iguchi. “Female Genital Cutting in Malaysia: a Mixed-Methods Study.” BMJ Open, vol. 9, no. 4, 2019, doi:10.1136/bmjopen-2018-025078.

[5] Obermeyer CM, Reynolds RF. Female genital surgeries, reproductive health and sexuality: a review of the evidence. Reproductive Health Matters1999;7:112–20.

[6]Catania L, Abdulcadir O, Puppo V, Verde JB, Abdulcadir J, Abdulcadir D. Pleasure and orgasm in women with female genital mutilation/cutting (FGM/C). The Journal of Sexual Medicine. 2007;4(6):1666–1678.

[7] “Medically Unnecessary Genital Cutting and the Rights of the Child: Moving Toward Consensus.” The American Journal of Bioethics, vol. 19, no. 10, 2019, pp. 17–28., doi:10.1080/15265161.2019.1643945.

[8] Lightfoot-Klein, Hanny. “Similarities in Attitudes and Misconceptions about Male and Female Sexual Mutilations.” Sexual Mutilations, 1997, pp. 131–135., doi:10.1007/978-1-4757-2679-4_12.

[9] http://artemide.bioeng.washington.edu/InformationIsPower/Pediatrics-2013-Frisch-peds.2012-2896.pdf

[10] The Law and Ethics of Female Genital Cutting Arianne Shahvisi, Brian D Earp.

[11] Current critiques of the WHO policy on female genital mutilation