Maybe antonym isn't the right descriptor. I'm wondering why the word 'misogynist' ('miso' meaning hate and 'gynist' meaning women (roughly)), is so commonplace but there isn't, to my knowledge, a word that means woman who hates men.
If you want to get technical (which I know you do), then philogynist could be an antonym of misogynist, but it's not the word I'm looking for. Misanthrope is close, except it means someone who hates all of mankind. Misandrist is the word I'm looking for, I think, except I'm not sure it's correct and I've never seen it in my life until googling for it tonight.