Two things I'd point out: first, that women's interest in these fields has not always been at the current (low) level. Second, that women's interest in these fields is higher (than the U.S. level) in certain other countries. It may be that the female interest level in those countries is the highest we can possibly hope for given the (alleged) cognitive differences between men and women. But even if that's the case, there's still room to improve in the U.S. I'll recommend this academic paper out of Carnegie Melon. Table 13-1 is interesting.
You are not listening to me.
And you're not listening to me. Maybe if I used all caps instead? I acknowledge that men and women, at the aggregate level, have different interest. I'll even cede that they may be partly due to physiology. Will you cede that they may be partly due to social factors and that those social factors may in fact be mutable?
Speaking purely anecdotally, all the women I've worked with in software development have been above average in terms of how hard they work. Some of them have been very competent; some (very much) less so. But none of them were slackers.
Lawyers and non-research doctors are basically overhead. You need them for society to function at an acceptably high level, but they don't really drive innovation. For that you need STEM guys and some management glue to organize them and turn the innovative vision into reality. More STEM guys (and/or gals) = more innovation = greater national prosperity.
Attitudes toward professions change over time. If you go far enough back most secondary school teachers were men. We may never reach complete gender balance in STEM, and I am 100% okay with that. That said, to the extent the imbalance is the result of mutable cultural phenomena it may be worth attempting to modify them such that women begin to prefer STEM careers at a higher rate than they do now.
For instance, this might answer questions like, "To what extent is the gender gap in STEM degrees caused by differing levels of aptitude and to what extent is it simply a result of preference?" We'd be comparing students with similar ability and aptitude. At least, to the extent a blunt instrument like the SAT is a valid proxy for ability and aptitude. What degrees do highly mathematically gifted and somewhat verbally gifted women actually pursue? What about men who are similarly gifted in both areas?
Stop trying to turn it into a fucking social issue, its a god damn evolution issue.
Then we would expect to see very little variation from country to country in terms of male vs. female interest in STEM careers, right? Is that the case? It may be the case there there are physiological differences between men and women on an aggregate level that give rise to some of the gender disparity, but you're an idiot if you don't think social issues also play a part. For instance, if it's all physiological then why was women's participation in computer science higher in 1984 than it is today?
With respect to why we might want to break down cultural taboos that keep women out of STEM fields, it might be because doing so could potentially both increase the quality of the U.S. STEM workforce and/or allow it to increase in size. If one half of your population opts out of a given profession then that shrinks the pool of potential talent.