There's a big difference between a woman who is at her strongest and best under the protection and guidance of the man who loves and respects her, and a woman who believes that she and every woman are inferior to.every man.
I've found far less 'internalized misogyny' in women who've embraced the inherent strength of their own womanhood, than in women who've bought into the lie that we have to live like men to be their equals.