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I feel it's because furries exist at a bizarre crossroads of many bad things.
1st. The large majority are furry because of some sort of social failing. The heart of furry is escapism (if I was a wolf, I'd be so cool). They have victim complexes likely because of that. People in general have an intuitive feeling for this sort of thing. We ALL know that one guy who gets made fun of all the time, seems bothered by it, might try to fight back pathetically, and ends up under more ridicule. People sense this weakness and then it's a field day on them. The result is always the victim in his victim-mentality always failing to react in a way that ceases to expose weakness. Vicious cycle of being made fun of, retaliating poorly, and getting it all the worse for that.
2nd. Furry becomes a personal identity. You adopt a label of "who you really are inside." Esteem is built on personal identities. Thus, attacking the rainbow colored gay wolf for being furry assaults his personal esteem. He then rushes to cling to that self-esteem. See above for how that goes.
3rd. Furry is weird. It just is. Most people do not find dog-faces sexually attractive. If you do, you are weird, and thus you provoke the reactions any weird thing gets.
4th. They're a minority most places they go. You can't gang up on a sizeable chunk of a population without some serious backlash. But if they are small enough . . . well, talk to the Jews.
All of these factors come together in a perfect storm of Furries being an ideal and easy punching bags, deserving in some cases or not. Well, deserving in a lot of cases, mayhaps.