In game design, if you build player characters or factions that have
exactly the same abilities, you have a balanced game where everybody has the same opportunities, but it makes for a pretty dull game. We call this
symmetrical balance. However, if you build player characters or factions that have different abilities, you can still get an equilibrium where everyone stands an equal chance of winning, like a game of rock-paper-scissors. That is
asymmetrical balance.
Men and women usually have different goals. Given their role as male, men "win," from an evolutionary standpoint, by maximizing reproductive quantity. Hence why polygyny was so common among rulers in the ancient world. (If you've got a better idea about how to swarm your neighbors with loyal warrior-sons, I'm all ears.) Women "win" more by a balance between quality and quantity. On the one hand, they need to pump out as many of their own children as possible, but on the other hand, because of the resources needed for gestating and nursing children, women have to make sure each child stands a maximal chance of survival. Hence, quality. Consequently, both sexes have different priorities in childrearing. But neither set of priorities is ever "winning" against the other, because they counterbalance. The male's goals keeps the female's in check, and vice-versa. If you remove one, the other runs rampant. It would be like taking "rock" out of the paper-rock-scissors game; scissors would just always win or tie.
The problem I see with feminism (and Marxism generally) is that it talks as if there is only one type of social power, namely the one that most characterizes males. But there are other forms of social power, not so easily noticed, that women have long employed as a way to counterbalance male forms.