An interesting programme I watched was "Horizon: Is Your Brain Male or Female?". The title is a bit crap but some of the experiments were interesting, like the observation that Barbary macaques seemed to be drawn to toys along gender lines. The boys going for the cars while the female macaques preferring the dolls.
The most interesting experiment, I thought, was when they observed how adults treated babies. For instance they tended to treat the boys as more robust pushing them more in physical environments while being gentler with the girls. They dressed up the babies as boys or girls so the same child was treated differently when presented as a different gender.
I guess the general outcome was that it is a bit of both nurture and nature, as pretty much any complex thing is. My thought is that culture is the overriding factor, different cultures or times can choose whether a profession like nursing is "for" men or women.
According to Naomi Klein in The Shock Doctrine part of the reason to exclude Baath party members from the Government was to simply sack nearly everyone in the Iraqi Government. The US had an agenda of privatising Iraq and freeing its markets and it didn't need a local Government to slow them down.