But we can ask them, right? We can ask e.g. nurses and computer programmers whether or not they loathe the choice of their profession. If there is e.g. relatively more computer programmers loathing it than nurses then you have an evidence of culturally pushed preference (towards computer programming, in this case), regardless what the gender ratio in those fields is.
"it matters a whole lot for purposes of an individual figuring out how to create a good life for themselves"
I already responded to that, basically I don't think it matters for an individual: https://news.ycombinator.com/item?id=18381148
For example, if you ask a women in a very poor rural region of India whether she wants to become an engineer, she might value the possibility far less than she would if that career choice was a realistic, valuable option for her in her current situation. Other typical examples would be slaves who prefer to remain slaves because they are not in a position to really imagine life as a free man, women who state that they prefer to wear a Burka, because they have been raised that way, or a peasant in feudal times who would only have very modest aspirations because he could not possibly imagine living the life of a nobleman whose higher rights were given by God.
More generally speaking, the underlying problem is that the so-called "preference satisfaction view" is false.[2: p. 4] That's the idea of classical welfare economics that people prefer what's best for them. As Broome puts it, nobody really believes it, but it forms the basis of many arguments and theorizing.
So you cannot just ask, although surveys can be used as (potentially fallible) indicators.
[1] https://www.iep.utm.edu/sen-cap/#SH1b [2] https://www.cambridge.org/core/books/ethics-out-of-economics...
I mean, when I talk about asking, you can make education part of the asking the question. I am certainly not against more education, like showing what is it like to be engineer.
I might disagree with women who decide willingly to wear burka, or decide to be slaves, even if they have a different choice, but as long as they make it freely, I have to respect that choice.
It seems to me that these problems should be addressed with education first, rather than by imposing someone else's preference on people (which is my main worry here). Therefore, that some rural Indian women might decide differently is not really transferable to decisions made by well-educated women in western postindustrial societies.
So I usually look for common explanation for gender segregation that work both for women and men. 87.4% gender segregation for men and 87.6% for women is rather extreme, but it is also quite obvious that either there is a common cause or a massive coincident that both men and women end up working in mostly single gender work places.
It would appear to be unfalsifiable. If someone is sure they don't want X, and you're telling them they really do want X it's just that they've learned to be pathetic their whole life and now their entire thought process is inferior to yours, that seems not only like pseudo-science but actually a dangerously extreme belief.
You said you don't understand why other people care so much about sorting out what is biological and what is cultural in origin. A few people (me included) engaged you in discussion to explain why other people might desire to get a better handle on this.
I have no idea why you jump from that to some idea that you personally are being expected to do anything for anyone other than let such research exist so that those who do care and need it can find such info.
Basically because if it is cultural, it may be a form of brainwashing and the expressed preference may actually be something they loathe, but don't feel empowered to reject.
Whether or not you think this matters for purposes of making policy, it matters a whole lot for purposes of an individual figuring out how to create a good life for themselves.