I was surprised when after going through random surveys by university, I found that mathematics had 25% bigger proportion of women than engineering or computer science. To me, pure maths are an epitome of logical thinking(I could not do pure maths, I am just not suited to it) and it is an established fact that most women prefer feeling over thinking careers. But, on the other hand, I have three girl friends who do maths. One is really depressed about the subject, two others are quite indifferent. I am sure there are plenty who enjoy pure maths though.
Honestly, I see those ads by Google being sent to my mailbox around September-November where they even have grants to get more women in STEM. Those women who attempt engineering careers could actually get into Big 4 a lot easier than we men can. Recruiting of women is quite fierce but due to low enrollment rates in engineering discipline, very few women are snapped up by tech giants.
Also, aptitude is important but even more important is really wanting to learn about engineering and when you combine those two together, very few women want to go this route. All the girls in CS class are introverted, thinker types(I would dare to say we have a few feelers though) and are just different from regular feelers.
However, I do not think that encouraging women to do STEM is working very well. We had people who came to school and talked about careers in science, engineering but most women seemed to be unaffected by the prospects and just went with their hearts mostly. Some probably gave in(I can see some very unhappy girls in my CS course) and as a consequence either found pleasure in the major or silently feel not in their place. I believe that women who are suited for STEM careers do not need additional recruitment to choose the particular major. As a final note, my class in school was 50/50 girls and boys. None of the girls chose STEM field, none. We had recruiters but none went with it.
EDIT: Just to add why girls did not go to STEM. Because they were lazy. That is hard truth but truth nonetheless. But so were a lot of boys. So no sexism here. I was never called smarter than my peers by my teachers but I was repeatedly called 'hard-working and determined'. I studied more for my science classes and set my goals to get straight 10s in my science classes. And I did but it was hard. Also, I know several women from higher up years. Most of them are in medicine(highly competitive to get into state funded place), one is in chemistry and one studies veterinary medicine. I know no one who studies CS or engineering though. My data shows that if a woman is good at science and excels at school, she will choose medicine over anything else.