I don't think conservatives hate women; when we use those terms, I think it cheapens the debate, because the automatic reaction is going to be "I have a daughter and a wife. How could I hate women?"
I think that the uber conservative male views women more like a very highly evolved pet. Lovable, but not quite capable of complete cogitation. More like creatures that need to be protected from the evils of society and from themselves than objects of hate and disdain. To me, this is the problem, not hate.