I feel much closer to my fursona when I pretend to be her. It's fun, too.
I am a tiger
Yes, Saskia, furry is something fun and different.
I picked the jaguar avatar out of the list of options when I created my own profile because I liked that picture best. I think that any kind of feline would be a good choice though. If I ever draw my own fursona someday, I might have some kind of mix of different types of felines. Cats for the win!
As for the original post that started this topic, I can only speak for myself. I accept that I am human and simply like animals and the idea of anthropomorphic animals.
As far as I know, most furries accept that they're human and merely like to pretend.
People who see themselves as being something else and merely having a human body usually call themselves otherkin, therians, or vampires. (Source: Wikipedia article on otherkin).
However, even though I accept being human, I also believe in God and in Heaven. So I think it would be awesome if furries can be their fursonas in Heaven and have the ability to change shape.