Winning being the operative word. UF is in the top 5 All Sports every year if they aren't # 1, so lots of teams get beaten by them. It still seems that more people hate Duke in Basketball than they do anything else, but maybe thats just me.
Winning does gather some hostility, but I suspect Florida's distinction goes back to Spurrier and his personality.
Most of the hatred goes back to the old Head Ball Coach.
Speaking of Spurrier, he deserves a lot of credit for Florida's basketball program being where it is. Most schools football and basketball programs go against each other, but Spurrier helped Donovan in the early years with recruiting.