Youre fundamentally misunderstanding what a power structure is. It’s not merely a group of individuals who are misogynistic (that is commiting acts of: violence against women, discriminating against women, subjugation women, and perpetuating hatred and prejudice against women) its a pervasive continuous problem across all levels of society and perpetuated by all functions of society. Misogyny exists so universally in our society that every single woman experiences it throughout their lives beginning as very young children. Our own parents teach us misogyny, our education system reinforces misogyny, our media shows us misogyny and so on. There’s no woman who doesn’t experience it, it affects all women as a class.
No such system exists that discriminates against men as a class.