StereochemPurist I think Mitchell addresses that when he says that we simply don't know, when it gets to things like interest in STEM, how much is down to biology and socialisation.
Anyway, I don't think it follows that because we may have a tendency one way, that that should be encouraged. We have a tendency to crave fatty sugary foods but we don't think it's healthy to always give in to that tendency. A biological basis for male aggression doesn't mean men should be encouraged to be aggressive, and a biological basis for a nurturing instinct in women doesn't necessarily mean women should be consigned to home-making.
Spencer Greenberg talks about a meta-analysis of studies on sex-related personality differences here and he says that most people sit in the overlap area. Where you find a marked difference is in extremes - for example, it is rare to find a man who's a psychopath but it's practically nonexistent among women. Also, he found that men will express interest in people depending on how the question is asked. So I think you're right when you ask what exactly is meant by 'things'. I'd also like to know what's meant by a nurturing instinct - is it the feeling of responsibility, or the enjoyment of looking after others (which, after all, is often tiring and unpleasant). Do women end up with care work because they feel it has to be done, or do they do it because it actually makes them happy? My guess is that both men and women are happy hugging their well-behaved kids and neither men nor women particularly cherish dragging screaming kids around a shop or cleaning toilets.
It's also interesting that when a stereotypical woman's job like cooking becomes prestigious and well-paid, it becomes a job more likely to be held by men. It's true that being a chef involves martialling kitchen staff and maybe that draws on stereotypical 'male' skills, but it still undermines the idea that, because a task tends to be carried out by one sex in most cultures, it is somehow biologically tied to that sex.