Oh dear daisy. It was an incredibly offensive thing to say. I suppose I would have a problem with anyone who has a problem with feminism, not only that but it seems to betray a wider, more insidious, hostility.
I am about to celebrate the fourth anniversary of splitting up from my XH. He always knew I was a firm, Guardian-reading feminist, bleeding heart liberal and proud of it. It was only has his respect for me diminished to nothing that he started to trash this part of me as if it was a) somehow a surprise to him b) something to justify his contempt.
Your DH is choosing to believe that feminism equals man-hating, obviously because that suits him. Presumably when sober he can see that this is not true. But it doesn't really matter what is true or not in this situation. I think your relationship has probably moved beyond political discussion.
I'm looking back now and thinking, if..., IF I ever got myself another partner... and that feels a long way away right now, he would have to be a feminist. I couldn't be with anyone who did not embrace feminism - just equal rights, that's all it is.
However, Feminism is not your problem here. You have probably interpreted it correctly as a signal of his lack of respect, or worse. That's the problem here. The decision for you is whether to put up with it (Um... why the hell should you?) or whether to make a stand and say you will not be spoken to like that, drunk or sober.
Sorry OP. Are your children small? Splitting up is a very hard prospect, and that may be way over the horizon, but I think you have to make it clear to your DH what is at stake for you.