My guess is that they confuse furries with people who are sexually attracted to animals or animal characteristics.
In reality, furries are people who partially or fully identify with what native people would have called their spirit animal and modern furries call their fursona (except with more or less human features, because they meld what they see as their spirit animal with their human self).
But because drawings of fursonae exist, rule 34 ensures that there is porn of them. Some people really like that kind of porn, unrelated to whether they're furries or not, and I believe it is those people the hate is directed at.
As for why, I would guess it's something like "how dare you sexualise animals!" (or maybe even a subconscious "how dare you make a drawing of what I believe is supposed to be an animal that is actually sexy to me!", similar to how some conservatives are so vehemently against homosexuality because they secretly feel tempted, and then get caught at a gay orgy later). And/or they see it as something like a gateway drug to bestiality (sexual abuse towards animals).