StrikerTheNoble, here's the problem with your idea of the differences between men and women.
Men are not entirely built to be 'stronger' as a whole. Women's lower body strength is superior. We also have a higher pain threshold. We're better at long distance endurance. Our brains are also more analytical (one of the reasons why we tend to be better at distinguishing social cues), and we work better in teams. However, even these differences are slight, because in reality whenever these statistics come up... the differences between men are greater than the differences between men and women. It's poor statistical reasoning when people bring up these so called inherent differences and then make broad ideas about how the world should be like.
Speaking of our hunter AND gatherer ancestry, men and women were in a highly eligatarian society, and a good amount of tribes were actually a matriarchy, where the woman is the head of the household. Men did go hunt, but women comprised a large portion of the diet from what they gathered. It's actually, interestingly enough, why men are more likely to be colour blind. The evolutionary theory is that if a woman was colour blind and would accidentally pick a poisonous variant of something, then she'd have eliminated her whole family once she cooked. If a man was colour blind, it'd have less consequences on carrying on his genes.
Also, our hunter and gatherers were a lot happier than we are now; they had far more leisure time, and less war. They had more sex on average, they dedicated their time to music and arts, they passed down stories, and developed their culture. There was a division of labour, but the range of their work was far more limited. Hunt, gather, raise children (both parents did), have fun. It sounds like an awesome lifestyle. It was! However, the climate didn't allow for this nomadic lifestyle to continue. For some reason, we had to settle, which led to a decrease in lifespan and leisure hours, and some would argue 'sowed the seeds' for future warfare, slavery, and even sexism.
However, agriculture was only possible (and probably saved humanity's butt) because of one woman whom we know as the Mother of Agriculture. She must have realized that where they would discard the seeds would be where the new plants grow, and from that she would have experimented and voila, taught it to the rest. Does this mean that men are inept at growing things because it was a woman who did it back then? Definitely not. However, growing crops and farming is tough work. Men and women did it, but now the division of labour became more stark, and because women had been designated to take care of children and thus the home, it sprung a lot of issues between the sexes that for a large part of our evolutionary history was not there.
The topic is a lot more complex than can be argued here, and it's one theory. However, the point I want to stress and close with is that these differences are exaggerated. We're all more likely to be average at what we do; when people talk about 'men are better' they're looking at the exceptional ends of the curve. Most of us are not in there. The idea that if you had two of the world's best mathematicians, and one was male and one was female, that the male would probably be better given the advantage he has in his neurological make up, that that should speak to the rest of us is just nonsense. The majority of people, when taken as a group, perform on average. Men and women are on average, average at math. We are not that much less unlikely that we'll score around that, and it's not that unlikely that we'll be outperforming some men at math. People are very complex, thus that we far more differences between men, than we do between men and women as a whole.
That's why the idea of wanting 'men at your back' because you think they'll be better at something, doesn't really help you in that matter. You're not likely to have the world's finest working with you, and people will have their strengths and weaknesses on any given project. We're not uniform robots. You hire people whom you think would be qualified for the job. The problem is these kind of ideas bar perfectly qualified men and women from attaining the careers they're suited for.