I agree with the sentiment in what you wrote, L.J. Before I had a son I thought that a lot of what we define as boy and girl play was heavily influenced by society.
There is, without a doubt, societal pressure when it comes to gender roles. But young boys and girls are different. All you have to do is watch them play and interact with each other. If they are given legos, they will often do different things with them. Boys also have a disturbing propensity for conflict toys (light sabers, spaceships with guns, “action figures”). My son’s favorite movie was Top Gun which he watched countless times (looking away during the love scenes).
Boys play differently than girls do and the hierarchies they form are different.
One thing that men excel at is aggression and violence. As a man, I am sorry to say that my gender is responsible for the vast majority of the violence in the world. Some people have proposed an extra tax on men because of the cost that society incurs because of the male propensity for aggression and violence.
Gender differences do not translate into professional limitations. Except in edge cases, men and women can excel at the same jobs, especially those in math and science.
Even in areas that require aggression and violence (military special forces, for example), there are women who have the necessary temperament (although in this case, there will always be more men).