I've got two sons, how do I raise them to compete in this?
The good thing is of course that individuals are always individuals, men don't have disadvantage when applying to schools.
Also, bringing up Finland again isn't bad idea, since here's almost none gender inequality in laws: the only law that puts men and women in different position is the conscription. The female-euro (80c) is forbidden in law, the reason women get less salary is that women work more low paid jobs (which of course is a bad thing, but not due to the legislation). Of course there's things related to child bearing, but it's harder to tell of them whether they are or not discriminating against women.
So, I'd dare to say that most of Finnish inequality comes from the attitudes and stereotypes people learn and keep up. Women are weak and follow only their emotions. That's why women can't be leaders, unless they are like men of course. Similarly men should be strong, and not some whining crybabies. Violence is sometimes pretty good option for men, if someone for example questions your manliness. It does two folded job, you both silence the other party, and also prove you're a man!
I don't know so much about other people, but I have never been that fond of stereotypes. I wanted to be in textile work rather than wood work in school, but my sister went through lots of arguing and frightening to get me choose the correct one. Also, I was told at school that men are evil, because we want to wage war. Throughout my life I've been also hearing how it's my duty to go to army, also from the same women who thought that that's why men are evil.
There's quite many more small incidents I could tell, but I'm not going through the trouble. Also,
the point of me telling these isn't that they are so bad per se, saying this just to prevent the "quit whining and be a man"-stuff.
I'm telling these as an illustration of how society teaches people to be men and women. As a result of these lessons learnt women will choose to become nurses and step down to make room for men. Men on the other hand learn to beat each others and that they can't show any weakness. As a result of these lessons women are underrepresented in all the leading places and men overrepresented in jails, suicides and alcoholics.
Someone's sure to say something about blaming society for your own faults. Well, that's not what I'm doing, I'm well educated, I don't practice violence, and my alcoholism is well under control.

Speaking of individual responsibility here is mistake, since I'm not speaking of individuals. It makes
some sense to pick a woman and tell her that it's her own fault she isn't CEO of a big company, since there is no law against it. It makes much less sense to say that the small number of woman CEOs is fault of women.
It's similar when you think about smoking for example: no individual case of lung cancer can be ascribed to smoking, no matter how heavy smoker the patient is. But when you look at the group of smokers, it's a fact only tobacco manufacturer can deny that smoking causes cancer. Or you can take another group of people whose poor success is mostly due to the attitudes. African Americans for example.
There has to be some reason for the fact that men are (or are about to be) more weakly educated, drink more, use drugs more, go to jail more, kill themselves more etc.
Btw. the above post wasn't directed to you Mathilda, but if I'd have kids I'd probably try to raise them be humans and individuals.