I don't know what your environment is like, but I notice a lot of people who are pointlessly aggressive and competitive, or who premise their aggression on being right about something they're actually wrong about. That doesn't make these people stronger and it doesn't make the world better. It would work better if everyone just focused on doing their own best job, and constantly checked themselves for correctness, rather than acting like they're never wrong, tearing other people down and trying to make themselves look better than they are. Those activities are not producing anything real.
Most of the time we are really all just trying to get by and perhaps achieve some shared goal, there is no game to win, and the people who are acting that way are just being asshats. It is not somehow clear-minded and objective to constantly strive for "supremacy" by aggression toward others, it's just messed-up and insecure.
(And what gives with implying that weakness is inherent to women? That's something that has no proof at all.)