I think there are a few reasons for this.
Firstly, gender has undergone a change in definition over the course of the past century or so, to include gender expression and gender identity as separate concepts from biological sex.
I know sexuality wasn't mentioned in the original post, but I've seen it in the comments. I think that, as society has gotten more tolerant, it's given people the opportunity to explore attraction more in-depth. And as it turns out, it's a lot more complex and dynamic than just "I like girls" or "I like boys".
In the cases of both gender and sexuality, brevity is important. Xenogenders and neopronouns are very difficult to keep track of, and trans and nonbinary people need to acknowledge that. Sexuality also doesn't need to be super specific. Each general category can have a bit more specificity, such as pan being a subtype of bi, or demi being on the asexual spectrum, but any more than that can get really confusing for people.
As for people identifying as animals, there's 2 routes you can go here: furries and therians.
Furries typically identify as human. They have personas and sometimes suits, but they ultimately still see themselves as human.
Therians identify, internally, as an animal or creature of some sort.
Please do remember that none of this is new. Different cultures have had different gender expressions since before our species existed, and nonbinary people, trans people, and therians have been around for millennia. Furries have sorta been around for millennia as well, but the modern fandom started in like the 70s. As for sexuality, I mean, there were most likely dinosaurs that were gay.
