One of the things I've learned over the years is that people can't hear the same arguments used against them in their own words. What I mean is that it doesn't matter how long an argument has been used to hurt you, it's still just as easy to use the same argument to hurt somebody else.
Recently I had the "pleasure" of reading a comment thread in which several transgender people were writing about therianthropy. The consensus was that therians are "mentally disordered" and "psychologically disturbed," and that they need therapy to work through their feelings rather than affirm them. The one person who called these out as being the exact same arguments used against transgender people was sharply downvoted.
I'm not going to sit here and say that therianthropy and transgenderism are automatically directly comparable. I do not believe they are, for many reasons. Appropriation of transgender language and struggle and skewed understandings of privilege are reasonable things for transgender people to be concerned about.
What we do not need to be concerned about, however, is whether or not somebody who believes something about themselves that harms nobody should be considered "mentally disordered." When we get up on a big soapbox talking about how weird and crazy other people are for things that do not harm us, we are doing the same thing as people who define transgenderism as a mental disorder. And no, that's not cool.
One of the major reasons transgender people get so irked about the subject of therianthropy is that comparisons between being transgender and "wanting to be an animal" are involved in some of the arguments used against us by bigots, and it's a common trope in transphobic humor (South Park was an awful example of this). Although this is something therians could be more sensitive about, we also need to recognize that the problem is not the existence of therians. Bigots are going to make that comparison anyway, and with our greater visibility transgender equality will still chug along.
I remember around seven years ago being at a panel discussion in which there were three same-sex marriage advocates who were insisting that same-sex marriage would not lead to polygamy. As polyamory gets more play, I see this counter-argument less and less... and it hasn't impeded that fight, because polyamorous people and polygamists weren't the ones holding the movement back. In the same way, therians are not the ones preventing transgender equality, and it makes no sense for us to spew such venom over that community just for existing and wanting to be treated with respect.