Maybe you could use your current gender, but for some people they want to include that variability in their identity. Just because they are also male/female/whatever doesn't change that they have identified as something else in the past, and they want to include that in their current self.
Is all attraction about looks? There are men who look feminine and women who look masculine and intersex people who choose to dress one way or another. And it's not true that the only two visible genders are male and female. There are trans women who keep their beards, people who dress entirely androgynously, there are cis men who like to wear pretty dresses but still identify as male. I think saying 'all people conform to these two things' is dismissing all the people that do. It may be a majority, but not all.
I tend to think of it like this (I am assuming a couple of things about you, but they are likely to be true, also sorry, this is a bit gross): Image having sex with a puppy. You may love puppies and think they are cute and you want one as a friend, but that is still revolting and not something you would ever willingly do. I wouldn't say 'oh you just have a low libido', its that you just don't have any reason to. You could argue that you can have low libido to anything because it is just a lack of desire, but then maybe there should be a descriptor for something totally outside that scale.
So you think people shouldn't try and find others like them for support? Being part of one society does not prevent someone from being a part of a different one too. I do think that very insular societies can be unhealthy, but that doesn't mean that groups of people with certain identities or issues can't have a group around them.
Sorry, perhaps I phrased poorly. There were large groups of colonialists that went to the Americas due to religious persecution, Quakers and Puritans and so on.
Treating their perceived identity as mental illness and something you want to make them fix is the first way you make them feel rejected. Yes it is odd, but is it harmful to others? If the biggest issue with how someone wants to be is that others hurt them for it, then are they the ones that should be made to change?
I'm not saying that thinking you are literally a dog/cat/wolf/space whale isn't potentially an issue, but I do think that making them feel safe and welcomed is the first way to help them.
Also side note - not all beast/whatever-kin actually literally think that they are an animal/other being. For a fair few of them it is an equivalent of belief in reincarnation (they have been an X in a past life), which is usually not treated as mental illness. When you get to that point then you start having to argue with religion, which right now I'd rather not do.