The fact that you can only look at this as a zero-sum binary where either "men rule" or "women rule" shows how deeply indoctrinated you are into the social system of patriarchy - a dominance based hierarchy with men wielding more power. How about a culture where nobody rules and people work together to try to treat each other with respect and without making assumptions based on immutable traits?
Until 50 years ago there were laws on the books that codified women's second class status, so no, it's not quite an equal amount of oppression. But that being said, it's true that "the fight" is not against men - it's against the entrenched dominance hierarchy and the way that harms us all.
"So, what does a contemporary partnership-oriented society even look like? Nordic countries such as Denmark have the closest approximation in modern times. Denmark is considered one of the happiest countries in the world by the UN World Happiness Report. One of the reasons may be that Danish schools teach empathy as a part of the regular curriculum, and provide weekly opportunities for students to help each other work through problems with the assistance of the teacher, based on listening to and understanding each other.
A key element of Danish culture is hygge, which could be defined as “intentionally created intimacy”. “In a country where it gets dark very early in the year, it rains, it’s gray, hygge means bringing light, warmth and friendship, creating a shared, welcoming and intimate atmosphere.” One of the elements of this is discouraging competition between individuals. Instead, students are asked to strive to do their best, using only themselves as a metric for improvement."
