But both incidents, ultimately, have less to do with whether Sanders is sexist than with how persistently and profoundly uncomfortable many Americans are with the idea of any woman seeking power — especially as president.

One of the ways Warren’s opponents disparage her is by attempting to portray her as Clintonesque; she’s being “Hillaried,” a term coined the moment Warren entered the race. As the field narrows and competition intensifies, supporters of Warren’s rivals have sought to associate her with the “establishment,” painting her as a corporate shill, an out-of-touch elitist, a plodding technocrat, a greedy lawyer — a backstabbing, untrustworthy woman whose individual ambition is harmful to the greater cause of defeating Trump. Republican and Democratic activists alike have used her bungled attempts to address the harm done by her claim of Native American ancestry to tap into long-standing “lying Hillary” narratives.

No one can argue in good faith that Warren and Clinton are exactly the same in their personal attributes and behaviors, political positions or policy ambitions. They are both lawyers, and both served in the Senate. But for the majority of her public political life, Warren has consistently been far to the left of Clinton. Where Clinton was accused of palling around with wealthy donors, Warren has relentlessly outlined how she would break up their monopolies, regulate their industries and shrink wealth disparities favoring the ultrarich. The two women have strikingly different theories of power, which shows in their choices of words, advisers and policies.

The most significant point of comparison between them — and one of the only ways they are actually alike — is that they share the experience of being highly ambitious women who chose to try to lead the country.

That overlap is exactly where and why the question of Sanders’s “sexism” becomes such a political and cultural flash point. “Sexism” can describe a very broad array of discriminatory beliefs and behaviors, some obvious, most not. The Pew Research Center found that almost half of American women have personally experienced gender discrimination, and extensive research indicates how profoundly gender and race shape women’s economic lives and well-being. But most men believe that sexism is a thing of the past. (For that matter, a new CNN poll released Wednesday found that while most voters believe a woman could be elected president, twice as many women as men say isn’t possible, probably reflecting their differing levels of appreciation of the obstacles women face.) Sanders is not among those men: He acknowledges that sexism is real. But like many people, he seems to recognize only the most hostile and aggressive forms, ignoring the harms of bias, ambivalence and persistent trivialization.

In Sanders’s case, sexism is less about what he has done, said or understood — and more about what he hasn’t done, said or understood. He has, for example, a progressive voting record on abortion rights in the Senate, but he’s rejected abortion rights as a litmus test for Democratic candidates. He hasn’t, in other words, taken reproductive justice seriously enough. He claims to be aware of the problems women face, yet he also indicates through his words and actions that those problems may not merit his attention. His recent retracted endorsement of Democratic House candidate and leftist podcast host Cenk Uygur is a good example. Uygur’s history of rating women and making grossly sexist comments should have disqualified him from Sanders’s endorsement in the first place, regardless of his politics. Last weekend, when asked if he thought gender presents a meaningful problem for female candidates, Sanders answered, “Everybody brings some negatives,” and then cited his own age and Pete Buttigieg’s youth as additional examples.

Despite his decades in office fighting the “status quo,” Sanders’s 2016 presidential campaign was forced to address a lack of diversity in staffing, gender pay inequities and bungled management of staffer sexual misconduct. Sanders has apologized to the women affected and committed to “do better,” but when pressed to explain how he missed these problems, he responded, “I was a little bit busy running around the country.”

This sort of sexism isn’t a blunt hostility that’s easy to notice and criticize. It’s negligence and forgetfulness. It lives in negative space. This is why Sanders and his supporters — who are, some polling indicates, mostly women — are dumbfounded, whether in 2016 or today, by allegations that he might be a sexist or might have behaved in sexist ways. On the contrary, they argue, he has been a lifelong supporter of women’s rights, sees women as equals and calls himself a feminist. The focus of this defense is on how Sanders behaves, what he believes, how he feels and what his intent is.

But sexist biases operate free of intent, and they have impact regardless of whether people mean them to. These apologias look past how the women running against him interact with him and his campaign, the media and culture more broadly. This understanding of sexism — tied to what one individual does — denies the subtle complexities of sexism as a structural force, the role it plays in propping up misogyny and the ways men are privileged by these dynamics. Warren and Clinton, like other female candidates, have had to navigate this environment without seeming whiny or demanding or, worse still, “victims,” a reviled term that smacks of weakness and vulnerability.

Misogyny isn’t about individual sexism but how women experience the world, as philosophy professor Kate Manne argued in her groundbreaking book, “Down Girl: The Logic of Misogyny.” We need to understand misogyny as systemic hostility that includes punishing women for “not conforming to gendered roles and expectations,” she wrote. In the past, misogyny was largely defined as the hatred of women, an essential component of which was the persistent exclusion of women from positions of respect and power. Even women deeply entrenched in the status quo, those who curry and most benefit from racism and xenophobia, are subject to sexism, misogyny and patriarchal regulation.

The penalties women face are seamlessly part of the culture — resident in social habits and gender roles, economic incentives, traditional mores, and more. So are the rewards that accrue to men who, conversely, experience misogyny as patriarchal entitlement.

The #WarrenIsASnake hashtag is a good example. It brought back memories of how long it took Sanders in 2016 to disavow the toxic contingent of his supporters whom Clinton recalled this month. Serpent imagery is particularly tied to age-old perceptions of power and gender. The Bible’s association of Eve with the Devil in the form of a snake was a deliberate renunciation of powerful female divinities whose wisdom was symbolized by serpents, such as the Egyptian goddess Hathor, the Minoan snake goddess and Astarte, the consort of the Canaanite god Baal. The story, connecting women with a dangerous and cunning knowledge, demonized the serpent and the woman in tandem to rationalize a distribution of power that favored men. Online mobs may not be immersed in biblical hermeneutics, but because of such deep cultural legacies, a snake emoji is a cheap and easy sexist code. None of the current Democratic candidates would call a woman a serpent, but male candidates’ chances improve when others do, demonstrating the sexism and bias that studies have found to hurt female candidates. Is it sexist to tolerate other people’s sexism when it benefits you? We live in a world of sexism, diffuse and subtle, without sexists.

In this context, calling out sexism becomes treacherous. Each woman has to decide what her strategy will be. After the Sanders-Warren squabble, for example, more than 100,000 small-dollar donors contributed $1.7 million to Sanders, a record for his campaign, in what the press called a show of support against her claims of sexism. But if that loyalty is a material reward for Sanders, Manne’s analysis holds that it was also a material penalty for Warren.

The punishment that Manne sees as a key dimension of misogyny is essential to maintaining a patriarchal social order. Is it sexist to ignore the fact that our social order is patriarchal? Sanders inspires millions of people. His supporters are as diverse as any candidate on the left could want. His policy agenda — from health care to climate change — will improve women’s lives. Over a long career, he has consistently pursued progressive political ideals, and in the past five years, he has positively and irrevocably altered American political debate. But all of this has happened within a virtually uncontested patriarchal framework.

No critique of “the establishment” is genuine without an explicit call to dismantle systemic patriarchy. While Democratic candidates across the board are now more comfortable calling out white supremacy, they are not at ease combining those ideas and saying “white male supremacy” when referring to their own field. But how else can you describe the winnowing of the most diverse group of presidential candidates in the nation’s history to an almost all-white field of 12, with just three women — all of whom are now considered less likely to win than the men? If only half of the nine men still in the race had chosen to throw their skills, money and influence behind a woman instead of running themselves, this would not be the case.

Individual acts of sexism did not determine the outcome of the last election, but cultural misogyny almost certainly did. For the first time ever, Sanders leads in CNN’s national poll. Being accused of sexism doesn’t seem to have hurt him; it may, in fact, have helped.

CORRECTION: An earlier version of this article misstated the results of a CNN poll. The poll found that twice as many women as men said a woman couldn’t be elected president, not that twice as many men said that.