Aside from being socialized to expect to be bad at analytical problems, I'd suggest (from aggregate reading about stereotype threat, feminist issues, and my experiences growing up) that part of the issue is that there's a lot of fear of being seen to try hard and fail. It's perfectly socially acceptable (unfortunately) for a young woman to doubt her own abilities to solve a problem and in so doing, decline to try it. However, if she's seen struggling with something, she's likely to encounter derision, with the implicit or explicit statement that she's reaching out of her depth. A self-effacing attitude, or the semblance of it, is socially necessary, because while young women are allowed to be Smart, they are not allowed to be Arrogant. I can provide references for these points if needed, though I believe it's pretty familiar ground for those at all versed in gender socialization norms.

Into purely personal territory now - take as you will - there was a time (around 4th grade through perhaps 10th) when I was that afraid of failing. If I tried a novel problem (even if no one else understood it), and couldn't immediately figure out what to do to solve it, my (male) peers jumped in with taunts along the lines of "she's not so smart after all." There were several years where it felt like any major failure would utterly ruin my credibility as a Bright Girl. It was far easier to assess the difficulty of a new problem, and quietly decline if I didn't think I could handle it.

Concerning the gender imbalance on the nerd spaces of the internet, I could probably go on all night about it, but I'm about to pass out and start drooling on my keyboard. Maybe I will go on all night about it in a separate post on a separate night.