I'm not GLBT, just supportive and accepting of GLBT, but I'll do my best to answer anyway. For decades and centuries, people who were homosexual (gay or lesbian) or bisexual (attracted to both genders) were viewed with about the same regard as zoophiles are viewed with now. They were seen as sick, perverted, potential rapists, somebody who should be locked up, etc. Transgendered people were traditionally seen as confused, mentally ill, or whatever; transsexuality, the mismatch between physical gender and the mental/emotional gender the individual identified with, wasn't even recognized as being a legitimate state of being. It wasn't until the gay rights movement started in the 80s or 90s that GLBT people started to gain rights, recognition, respect, and legitimacy. It's a very small minority of groups and individuals that still see GLBT as mental illness, something that should be illegal, etc.

The GLBT community has made huge advancements in their acceptance in society. Zoophilia, the sexual orientation of being emotionally and romantically attracted to nonhuman animals, and zoosexuality, which is zoophilia that also includes physical and sexual attraction to animals, are still viewed as perverted, sick, a mental illness, potential for rape and abuse, etc. It is very socially rejected and taboo with a small minority of people being zoo and a very small minority of general society being tolerant and accepting of people who are zoo. Most of the rest of society rejects zoophilia/zoosexuality, and that includes people who happen to be GLBT.

It's most likely because of that social rejection and negative view of zoophilia that the GLBT community doesn't want zoophilia combined with their movement for rights and acceptance despite it being another alternative sexual orientation. It's similar to people of the black community not wanting the GLBT movement to be considered a civil rights movement similar to the civil rights movement of the 1950s and 60s even though it really is a civil rights movement. It happens all the time that one individual or group trying to gain their own positive reputation will shun another individual or group who still carries a negative reputation.

Many people view zoophilia/zoosexuality as abuse and rape of animals and think animals are incapable of giving or withholding consent, as the responses here show. The fact is that animals are fully capable of showing consent through nonverbal communication (growling, moving away, hooves, teeth, and claws say "NO"), and zoophiles, who by definition love and respect animals as true equals, pay close attention to that consent and lack thereof. They respect their animal mates/friends and only want to share sexual pleasure if the animal wants it too. It takes an abuser and rapist to ignore lack of consent and proceed to have sex with someone for one's own gratification, regardless of whether the victim is a human or nonhuman animal. Zoophiles love their animal mates no different than other humans love their human mates, and often view them as their spouses. They give them all the best care they are able, stick with them to the end of their natural lives, and would die to protect them. Sex for them is just an extension and expression of the love they share no different than a human-human couple. The fact it may be illegal where they live doesn't switch off their desire for that particular species of mate just the same as past laws making homosexuality illegal didn't switch off the desire of homosexuals to be with a same-sex mate.

It is true that there are people who rape and abuse animals, and that's just the same as people who rape and abuse human victims. Such people should be executed, in my opinion. It is never acceptable to rape any creature, human or not.

By the way, Sydney is correct that a person's human-oriented sexuality is independent from their animal-oriented sexuality, and that gender identity is also independent of sexual orientation. I know one person who is heterosexual with humans but bisexual with animals; I know someone who is heterosexual with animals but has no desire for humans; I know someone who is married to a human and also has an animal mate while the human spouse is not zoo (and obviously is accepting). Laws and societal perceptions of love and sexuality are all based on peoples' ideas of "what should be", not what actually is.

It's a bad idea to argue that people kill and eat animals without their consent so why be so concerned about consent when it comes to sex, because some people could see that as permission to ignore sexual consent and rape the animal since consent to be killed is ignored too, whether in practice or in their perception of zoophiles.