Anthropomorphism is nothing weird and considered a innate human characteristic. The furry fandom is all about anthro-animals, often these people have fursonas. Some people see the furry fandom as a way of expressing themselves. There maybe many who are not identifying with their own gender, stereotypes, have a differing sexuality or are different in another sense. Of course there may be people in the fandom for other reasons too. But as the number of LGBT+ type people/ alternatives in the fandom suggests this is a large factor.
There are some people may go as far as saying she/he is a otherkin or a therian or perhaps even transpecies (well I see the word around I don’t know if anyone identifies with it). This is technically not part of the fandom but some people may be a furry and also identify with one of these labels though I would say they don’t really make much sense. But its understandable that animals help people get to know themselves better and have a sense of identity. A person doesn’t necessarily have to look like a human, but still can be.