Why do many occupations show a gender bias?

Yesterday we had a question about the alleged underpayment of women in work, asking why employers would hire fewer cheaper female workers and would instead hire a larger number of expensive male workers. A large amount of discussion ensued. I'd like to approach the same topic from a different angle. Without doubt many occupations show a gender bias, and across the board it is apparent that women are more concentrated in occupations which attract lower hourly pay. What are the economic reasons why, when encountering low pay (or anticipating it at the start of their careers), women should not simply respond to economic incentives, and choose to transfer to higher-paid occupations to increase their earnings? I should say pre-emptively that I'm not satisfied with ideas that merely may explain the effect, as yesterday's question produced a proliferation of rationalisations and claims that lacked rigour. I'd prefer to see an explanation that attempts to be comprehensive, or supports contentious claims (such as those about women's productivity) with research.