Humans have combined human and animal features basically for as long as there has been any kind of culture at all. We have cave paintings of animal-headed people. It's a powerful idea, one that resonates with a lot of people worldwide.
That's where furry comes from, essentially. The modern furry fandom started with funny animal cartoons, like Disney or Looney Tunes. Cartoon artists and animators found that animal traits made for a great visual shorthand for character and personality. A fox is perceived as sly, an owl as wise. If you want a roguish character, an anthropomorphic fox fits quite nicely. If you want a wise old sage, there's the owl. That led to some artists getting their characters to deliberately act against type for the sake of subverting expectations, and eventually a whole subculture of indie cartoonists making "funny animal" comics with characters that didn't act like Disney types at all grew in the 60s. It stayed pretty small until the rise of the internet, which caused it to explode because suddenly isolated people who were into this kind of thing but never realized there were others like them could instantly find each other and communicate across the globe.
But at the core is still the same ancient idea that got Cro-Magnon hunters to paint deer-headed humanoids on cave walls. A mixture of human and animal. The cultured and the wild, rational and primal, juxtaposed in a single figure.
And no, it's not restricted to extreme fetishes at all. It's just that for everything involving humans, you'll also find a furry equivalent. So there's completely safe-for-work furry art, comics and games but there's also every possible flavor of porn (including some that are only possible with furry characters) and yes, extreme fetish stuff like rape and snuff fantasy.