I doubt furfaggotry is a family thing. Probably what happens is a parent notices that their precious snowflake is withdrawn and can't make friends, so they get it a puppy/hamster/kitten/bunny/whatever as a substitute "friend" in hopes that the lonely brat won't get into self-mutilation or worse. And since the animal is the only creature on Earth that doesn't hate the kid's fucking guts, the tard gets a little too attached to the critter to the point of wishing it could be that critter, and that desire eventually becomes a case of furfaggotry.
Source: wiktionary