This isn't the only way to get things done--for instance, architecture and engineering isn't included in the categories you listed and is super-important even for the day-to-day tasks of civilization, rather than the long-run ones. Still, the categories you list are big ones, and important for the day-to-day running and development of infrastructure.

That you included a solid, reputable source of data is great! But now I'm puzzled. The source I found--and linked--gave 10% women for a category that your source gives as 4%. Your source has 3.5% carpenters as women, but CareerExplorer has it at 7%: https://www.careerexplorer.com/careers/carpenter/demographics/. Similarly, speech-language pathologists show as 97.6% women in BLS, but only around 90% in other sources, e.g. https://www.zippia.com/speech-language-pathologist-jobs/demographics/.

I'm rather puzzled by how the numbers could be that far apart from each other. Someone can't count, apparently.

The numbers I've seen reported generally are in line with the examples I gave, which is why I said what I did. But it seems like it should be totally fair to use the BLS numbers, even if they determine them by survey and only get about a 70% response rate, apparently. You'd think that the methodology would be okay--even though response rates have been dropping over the last decade, 70% is still really good for a survey.

So, what gives? My initial guess is that people who are in highly gender-atypical professions are less likely to respond to BLS surveys, thus producing an even more skewed distribution than exists in reality. But it also could be that other methods use data sources that are biased in favor of gender balance (since that is more useful if you're trying to do market research or something) and this bias isn't corrected for.

I'm not sure how we would determine which type of source is more in error. Clearly they disagree pretty substantively.

Anyway, I retract the strength of my comment, because it seems like you did have a reason to give those numbers, from a source that ought to be reputable, even if the exact categories are a bit fishy, the reason could in part be bias against women, and the characterization of running civilization is wrong for the other reasons I stated. Even with those caveats, the original claim is a lot less preposterous than I had thought.

Thanks for providing the link! I'm editing my comment to point out to readers that they should look at your source. (I'm leaving the original text unchanged because people should see what prompted any discussion.)