Actually, I just read a book last night called something like '100 things about cats', and they say that females especially bond well with cats when they are single even if other people are living at home. For some reason cats are very nurturing and give some individuals who need a more calm and empathetic pet vs. the energy of a dog a sense of being OK. I am a lot like that with my own cat and find comfort in her when other people treat me badly.

All in all, you're not weird or a bad person for liking the empathy and happiness animals provide you. Of course it is important to reach out and bond with other people, but obviously ATM you are having a hard time and need more time to work on this. I don't know a clinical name for this however.