It does not follow logically that just because men and women are biologically different that those differences are necessarily significant with regard to career distributions.
Not necessarily (based solely on the axiom that men and women have different brain chemistry).
It is logically possible that the differences we observe in career distributions are more heavily influenced by other factors besides differences in brain chemistry.
Lets consider a sociology view. When it comes to inter-sex competition there is a sexual dimorphism where men competes and derive status over resources and women over social relations. This would causes behavior divergence for both boys and girls, especially during adolescence, where both sexes will do status-seeking behavior and favor career choices that best fulfill their goals.
That sexual dimorphism could in turn be caused by a different brain chemistry or by cultural values. From studies that look at different indigenous people, it seems universal that women select men based on a mans ability to gather resources, and men selects women based on their ability to raise and nurture a family. Inter-sex dominance hierarchy also follow those lines.
I feel you're being too permissive of the possibility that culture drives gender roles. It seems implausible that culture would cause every civilization however isolated to organize itself along very similar gender roles. I understand you are alluding to this; I just want to put a fine point on it.
Maybe, but it certainly doesn't follow that career preferences are the same or that culture is the primary driver for career distributions. Never mind that culture is a function of biology.