>However, if you check the ratio of people even moderately high on the Asperger’s scale among programmers, it is much higher than other more social profession but still a small portion overall. That difference doesn’t come close to explaining the gender gap.
That's why I included the part about the programming work environment generally being unpleasant and demanding. I didn't make the connection explicit, but "high paying job that sucks" is a preferential attractor for male workers. 90% of workplace deaths are men, men tend to do more things like "work on dangerous and dirty oil rigs", men tend to work more hours than women, and women tend to accumulate in more personally rewarding jobs such as teaching or social work. The end result is a gross earnings gap that basically disappears when you control for these sorts of choices.
So to be explicit: becoming a programmer is a choice that pays well, but is difficult work, requires a large time commitment to study, and is not intuitively gratifying. On that basis alone I'd expect outsized male participation.
>I’m not familiar with the gender distribution of introversion
In terms of big-5 personality traits, the gendered differences are that women tend to score higher on Agreeableness and Neuroticism. I don't think it's particularly relevant to this whole discussion, though.