You're treating it like well-established fact that people's career choices are based on gender identities which are fabricated by the environment they're raised in. Where is the evidence for this? Where are the oddball societies with female construction workers and all-male nurse workforces? If this is just an "accident" of the memetic evolution of societal gender tropes, then why is it so unilaterally consistent across cultures that have developed separately?

The biological explanation is, by far, the Occam's razor null hypothesis here. To be convincing, you would need to supply compelling evidence that children who have unusually low contact with traditional societal influence early in life make less predictable employment choices. Otherwise, this is a just-so story like all the rest of them.

Actually to prove otherwise you just need to find traditionally "male" roles that are no longer male dominated roles. Like teachers, lawyers, or doctors. All had centuries of being male jobs.

Or find 'male' roles in some cultures that aren't in others like programming.

You assume that careers are immutable in terms of the work involved, and the returns for the employee, through the ages. I don't think that's true.

I picked 3 examples where it is true though. The exception being teaching in the US specifically pays awfully but it pays pretty well/has good benefits in other western countries.

OK, let's look at different sets of people.

My argument is that you cannot expect uniform distribution of career choices either by race or gender.

You can't expect exactly 13% of cops to be african american or exactly 50% of physicists to be female.

Let's look at hispanics and asians.

Asians outnumber hispanics in STEM 9:1

Hispanics outnumber asians in History 3:1

Don't have links to hard sources at hand since I'm on mobile, but even anecdotally I think almost anyone would agree that hispanics are outnumbered by asians in STEM.

Ethnic chinese are strong in STEM not just in US, but almost anywhere. You can take any country with a significant chinese diaspora and you'll see the results are about the same.

Can you make a compelling counterargument that hispanics are brought up in a way that specifically encourages them to learn History?

Many asian countries culturally encourage STEM fields above all else so it's not surprising that they are both over represented in STEM fields and underrepresented in non-STEM fields.

I'm not sure what point you're trying to make here? That culture pushes people to certain expectations? I agree.