I'm not sure how you can merge the two theories that "Women are just better at people skills" and "Women aren't better than the best". The whole thesis is claiming that women are as naturally superior at people skills as men are naturally good at tech/STEM. Google is supposed to hire the best, and it's >50% men, so why isn't something that "hires the best" (in politics) still <20% women (e.g. US Congress).
So where are the places which are 90% women? Why isn't politics 90% women. Instead it's about ~20% and that's after years of campaigning & activism.
[1] https://www.dol.gov/wb/stats/occ_gender_share_em_1020_txt.ht...
I remember my time in the Harry Potter fandom, which is ~99% female. Boy, was there politics. I can remember some truly epic [1][2] incidents of Internet drama all driven by people seeking social status through any means of manipulation possible.
[1] https://fanlore.org/wiki/The_Ms.Scribe_Story:_An_Unauthorize...
[2] https://fanlore.org/wiki/Victoria_Bitter_Wank#Further_Readin...
How much counter-examples can you ignore before you say well maybe this "women are good at people skills, men are good at STEM". It seems like people really think "well men are better at basically everything"
In industries that actually are 50/50 or majority female, you do see a number of women in top leadership positions. For example, the president of the national teacher's union is a woman [1], as are the three co-presidents of the national nurse's union [2], as is my alma mater's (which only went co-ed in 1974) college president [3].
[1] https://en.wikipedia.org/wiki/Randi_Weingarten
Here's a UK survey of chefs: http://www.bighospitality.co.uk/People/Survey-finds-imbalanc...
It's almost like there's some sort of social factors which will ensure men get to the top!