The point is, in middle eastern societies, the realities of working in STEM don't impact the choices women make for their college majors as much. Most of them go to college before marriage with the expectation of not having a long term career in what they study (public colleges are almost always free there, btw). They decide what to do considering different sets of pressures in comparison to women in the west.

Women in more egalitarian societies make their choices under different pressures. They need more of a long-term plan for their career choice and they don't have as many children or marry or leave the workforce as early nor as often as women in the middle east.

Do note though that as more women get into STEM, the experienced and perceived discrimination levels drop dramatically and even more women make the switch. Also, I think it's useful to note that there has been a systemic reduction in what I call the level of "generational misogyny." I can confirm from my own experience that there is a huge difference in how older vs younger (<40yo) men interact with women.

Younger folks are way more egalitarian and some of them assume that they all get the same treatment from older folks but that is just not true. A 30 years old male researcher could have entirely pleasant and productive working relationships with both female researchers in his generation and male researchers in their 60s. He might not expect or understand the degree of hostility or discrimination his female colleagues face when dealing with these very same older researchers. I believe that as time passes and the egalitarian culture actually gets to the "top of the food chain," we will see a distribution that is more representative of male and female preferences without the added discriminatory pressure.

But time has already passed since greater sexism and males and females have already gravitated in two consistent directions - men working with things and women working with people, even when it defies traditional gender roles, such as computers and business. You expect that trend to change direction after some tipping point of sufficiently little sexism?

So, that makes you reach the following conclusion: "the more a society is egalitarian - say, Scandinavian countries, the more it forces women to do painting and arts".

Are you saying that "egalitarian" societies are in fact sexist, and that teaching schools/staff (largely populated by progressive left-wing women), are in fact preventing little girls from doing maths and learning C in their bedroom ?

A common hypothesis is that there are genetic and social/economic aspects that push people towards one field or another. If you make an effort to remove all social forces, and succeed, then the only forces left are the inborn ones- so their effects maximize. So, if there are any inborn differences in the distribution of interest in e.g. engineering between men and women, you would expect to see their effects most keenly in the most low-pressure countries. Inegalitarianism adds pressure that money is useful for dealing with.