For me, it's the fact that he's a freaking perv and that he only has eyes for Ann. Get a life, man! Or... cat... monster... thing?
I'll honestly admit that Morgana is my least favorite character out of the Phantom Thieves. He's better than some people, but still... there's more crap about him that I don't like than like. Definitely not a cat that I'd want to sleep with.