I really, honestly think that men are better at basically everything than women. As cliche as it sounds, I really only think women are useful for s** and making babies, and that’s only because men can’t do the latter at all.
If it’s a test of strength, then obviously men as a group win against women as a group. In a battle of wits, men do better anyway and that’s why almost all of the great scientists/mathematicians/philosophers of history are men. Even now, there’s only one woman who even bothers playing professional chess against men. In other fields, I think the competitiveness and emotional restraint men are more prone to (or at least, are raised to show) just gets things done better. Even in things typically called “women’s work”, men still have an edge. Most professional chefs are men. Men can clean at least as well as women, probably better in things that need elbow grease or lifting furniture.
In short, if there is a patriarchy, it’s one men have earned by being so kick-a** and for taking charge.