Why do they exist?
Well, Sit tight, Cause this explanation is gonna be long.
Furries are merely a subculture of a core less-unknown culture of people aware of their Personas. Persona is, To put simply, A mask. The image you create when interacting with people. Your tone, Your posture, Your appearance, Your name, Everything others see of you is considered your Persona. But people later realized that they could make another Persona of their own. One they would feel most comfortable with. And this, They make one. Nowadays, It's known as the "Furry" culture. The main reason being, Well, Many people like animals, No surprise they want their Persona to be one. But Personas are shapeless, Like the person's soul. Other than just animals, It can be inanimate objects or anything the person wishes. Even you with the name of "TheSussyFranchise" and the image of a knight is considered a Persona. The reason for Personas is not to act different, But to stop acting. Create a mask you feel right to wear. That's also the reason why there's a stereotype of "Original Character, Do not steal", It's because, Well, How would you feel if you just created the perfect self for yourself and some sloth just stole the idea? Exactly.
Hopefully even furries will realize that the idea of Personas exist in every living being. It's not just an animal thing, It's a soul thing.
I've found this answer only after researching deeply to both science and religion to realize the truth.