Misogny refers to a number of things, and I believe it applies here. Here's the definition.
Misogyny (<small>pron.:</small> /mɪˈsɒdʒɪni/) is the hatred or dislike of women or girls. Misogyny can be manifested in numerous ways, including sexual discrimination, denigration of women, violence against women, and sexual objectification of women.
I believe that misogny applies in the context I was using it in better than chauvinism, which is more a blanket belief than men are better than women. I was trying to describe the vitriol and discrimination girls face.