Just to get this clear - you are offering the Schmitt et al paper finding differences between the averages in the self reported personalities of men and women across various cultures as a general explanation for every field of work in which sex ratios differ?
Only explanation for every field of work across every culture across all of time? Lol, no. I'm not biting.
This all started with me agreeing with hapless Mr Damore, so let's stay focused on modern Western societies.
And here, I believe it to be a pretty good explanation. That does not mean this is the only explanation. "Environment" is not a single factor either, but comprised of countless factors. Persons might be simultaneously pulled into a field they're not really into (e.g. because more money) and pushed away from it (e.g. because sexism). And even when you get rid of sexism, as you should (or at least reduce it), the gender gap might widen, because people might also have become wealthier and freer to follow their actual preferences, rather than just money. That's what has been observed to happen, after all.
Also, how about rather than asking me to make sweeping generalizations that are bound to have errors (as generalizations invariably have)
you figure an example where this
can't be used to explain it and we'll see if we can agree there? A modern, Western society might be nice, because I'm not necessary familiar with every other job in every other culture.
Fine, but what alternative measure do you offer?
Since this all started on a level of a company (albeit a large one), I'll bring company-level examples.
You look at hiring statistics: how large chance do male vs female applicants have to get hired. (Might find something counter-intuitive, like "even though we have 3 times less female than male employees, female applicants actually have 3 times higher chance to get hired".)
You look at wages, while controlling for experience, hours and the like.
You ask people - all of them - if and what problems they've experienced.
And so on.