> push girls and boys to choose different jobs based on their gender?

Nowhere did I suggest as much. I am simply suggesting that the gender roles we ascribe to children early on leave permanent impressions upon what they choose, and maybe more importantly, what others expect of them.

by insisting on that suggestion, you are implying that this is harmful, that women choose incorrectly, and that it be corrected

No, women (and men) are not “incorrect” for having been misguided by their upbringing. Children aren’t to blame for the way they were raised, they have no choice in the matter. Those who influenced them in that way are the ones who are incorrect.

by what evidence or intuition are you inferring misguidance?

We have plenty of relevant examples of scenarios where, given the exact same set of circumstances, men and women would be treated differently for exercising free will in defiance of gender norms. There are still jobs, even in the most progressive parts of the world, where people are given different levels of respect just because of their gender.