The problem is that what used to be called nature and nurture are now sometimes found deeply intertwined in complicated ways (Cordelia Fine writes about this in her book about testosterone) so that something like "being innately drawn to certain types of work" is very difficult to actually empirically study.
We can't put new-born infants into an alternative reality where they would grow up completely without any social cues about what is suitable for women and what is suitable for men so that we could then study how their life choices would differ.
In our reality the cues are everywhere, though they are clearly stronger in some cultures than others, backed by open religious rules or laws, and the problem is how to try to control for all the subtle and not-so-subtle environmental factors. As one example, the recent thread here about messages in children's clothing demonstrates that even wear for infants is colour-coded and items with messages tell baby girls about being kind, about unicorns and about hearts, while messages for baby boys tell about heroism, boundary setting, and being active.
One could argue that infant clothing of this type might just reflect actual psychological sex differences, but the clothes are not picked by the infants themselves. So distinguishing between what might be somehow coded in our genes and what is added as external input is extremely difficult.
The other problem is that all research into sex differences has a built-in bias in the sense that it must be participatory because all researchers belong to a sex class to begin with. This bias is even visible in the name of the field (gender or sex differences), because there is no field called gender or sex similarities.
So when a study about something perhaps not even about sex differences finds some, it is those that will get stressed in the abstract, while studies of the same type which find only sex similarities but are really not about gender or sex to begin with, simply don't point the similarities out as actual findings. This is, I believe, not because of any kind of sexism (say, neurosexism), but follows naturally from our tendency to look for differences rather than similarities.
The human brains are also more plastic than was assumed in the past, and this makes it difficult to use brain imaging, say, as proof that some difference is innate or has some clear portion which is innate. Several studies have shown changes in the way the brain looks or functions as a consequence of past illnesses and past behaviours (the long-term memory of London cabbies in the past is a famous example here), so to the extent that women's and men's lives are differently organised by societies, we would expect observable differences, on average, in adult brains.
Finally, the whole history about women's place in various societies has always been built on the assumption of innate cognitive differences between the sexes, and those are still the ones used to argue that the natural place of women is in some inferior position.
For example, the most conservative Islamic scholars argue, even today, that women shouldn't be judges because women are more emotional and therefore less likely to decide cases on the relevant facts alone (which also ignores the way we tend to define emotions as excluding such emotions as anger from the list, perhaps because men show it at least as much as women.)
So it's quite likely that a focus on sex difference as innate is as or more likely to support the case against women's equal rights than for them, and because this is how such arguments have always been used in the past I hold any new ones to very high standards of proof.