It's very simple. A lot of kids like to make believe they're wild animals, and draw them, and dress up like them on Halloween and get-togethers with friends. It's a lot of fun. When they grow up, a lot of them still like to do all that. It's still a lot of fun. And of course, being adults, there will be adult themes used on occasion.
The criticism comes from people who think sex is the only fun adults can have, or should have, so if they see other adults having fun, they assume it must be sexual or an attempt to get sex. That's they only fun those people get.
Maybe they see furries having a lot more fun than they do and think we're having a lot more sex than they do, and they can't stand it.