Seems to me you're playing hide the ball a bit here. If it's the case that society conditions men to display confidence, then aren't we left to explain why _that_ might be the case? Why doesn't society condition women to be the more confident? How did we get here? The null hypothesis would probably be that innate gender differences created the current sociological environment, creating a chicken and egg problem.
This reminds me of the argument that women's under-representation in STEM fields begins during childhood when we condition them with toys that don't encourage spatial reasoning. This claim leaves a gigantic dangling question of "Why are toy companies and parents so damn bad at understanding what little girls want to play with?" The literature supports the intuitive truth of the matter: girls and boys find their toy affinities on their own without much input from society.
Incidentally, I think most people are morally taking the wrong tack when it comes to this kind of stuff. If you make a value judgment that having an affinity for leadership or spatial reasoning is Good, then you are no longer free to interpret the actual world without worrying that the data will show men are Better (or Worse). Why can't we accept men and women as they are, and stop pre-supposing equality of all measurements that we might consider desirable? If it turns out that men are naturally suited to taking leadership roles, who cares? It takes all kinds to make a functional society, and in the scheme of things, leaders are a tiny thread in that tapestry. I find the role of leader or mathematician to be equally valuable to artist, baker, carpenter, fashion designer, grocer, mother or father. Each of them is a valuable member of society that should earn a fundamental human dignity. In my view, admonishing women to pursue engineering is equally repugnant to demanding they avoid it! Let's encourage all of the women who find engineering or mathematics irresistible, but avoid fretting about the many who don't!