Avians are otherkin who identify with birds, generally, but I suppose it could also extend to cover other flying kin, like bats. Therian is a term that generally seems to apply broadly to animal kin, though I personally use it more to describe shapeshifters of a form (as I am—I only have one animal shift form, but I consider that my theriotype, whereas my kintype is Elven). I’ve definitely heard people with different opinions on what the word “therian” means, though. Other mods or followers are welcome to add their definitions, because I’m certainly curious as well!
As for hypotheses, I know why I’m otherkin, but it varies from kin to kin, so you’ll end up with a hundred different answers for every hundred kin. As such, I’m not going to answer, because I’m by no means an authority on how otherkin come to be, and my personal explanation is probably diametrically opposed to someone else’s.