We do know that women's brains function differently than men's. You're probably going to argue that that's because of some socially constructed imprinting. I think that there simply are differences.
So if you believe that biology has implied that women and men have different brains, what would you say about the studies showing that more men than women are at the extremes of intelligent (meaning there are more smart men than smart women, and conversely, more dumb men than dumb women)? Is that biology as well?
What about the idea that men's higher pay (on average) than women is due to being more aggressive about negotiating for a higher salary, and more willing to move on to another job that pays higher? Some research has suggested this, and if biologically, men's brains are different than women's brains, it's possible there's a biological difference for the gender gap in wages. (A similar mechanism could be argued for why men are more common than women in politics.)
There's also a study that has shown that women are more likely to follow orders than men, even when those orders harm another living creature. Do you think women are more likely to conform, even though it means hurting others?
Or do you strictly believe that men and women's brains are only relevant in activities that show men at a disadvantage? If you only believe that differences in men's brains disadvantage them, perhaps you need to ask yourself why that is the case. Then answer the followup question - if men and women have different brains due to strictly biological reasons, doesn't it probably follow that men will be better than women at some mental tasks? What if those tasks make men "better" at careers and politics? Using your premise that men and women are different genetically, even their behavior, it's a logical possibility.
But I tend to reject that theory unless proven otherwise. I think male and female behavior tends to be far more alike than many of us think. Here's why:
We've evolved to have huge brains. That has drawbacks. Women dying in childbirth is one of the more well-known ones. (Even painful childbirth stems, in part, to our large skulls.) But there are less obvious ones - for example, your brain disproportionately uses the calories you consume. The most frequently citied figure is that your brain is about 1/50th of your mass, but uses 1/5th of your energy. And we have an extremely long period of learning - we spend a disproportionate amount of our time as children, soaking up knowledge, instead of growing up and reproducing. From an evolutionary perspective, there must be a reason why we've devoted so much of our biological resources into carrying and supporting a huge brain that's born dumb. Sure, nowadays, brains are pretty awesome for survival (just look at all those modern conveniences, and the lack of modern worries such as being eaten by a cheetah at the local watering hole). But for the vast majority of H. Sapiens history, we didn't even have agriculture. (We developed agriculture in about the last 1/10th of the time humans have been around.) I'd hypothesize that what increased our survival was pushing more and more behavior from instinct (nature) to learned behavior (nurture), allowing the homo genus to adapt quicker and faster to changes in their environment.
There are biological differences in men's and women's brains. An obvious example is that men's brains tend to mass more (due to men simply being larger). But to use biology to explain all of those neurological differences, and to assume that behavior differences between the gender stems from those neurological differences is a huge leap. Especially since stereotypical gender behavior can and does change with the culture and with history. We have a long history of using "biology" to explain differences in human behavior amoung different groups, and we've often been proved wrong.
In summary (the too long; didn't read version): Humans do show gender differences in neurological anatomy. Some of this may stem from genetics. But it's far too premature to assign gender-typical behavior to genetics, and our evolutionary history and basic biology strongly suggests that humanity and its predecessor species found it very useful to have a large, very adaptable brain. A brain that nowadays can soak up many stereotypical gender roles from culture and act accordingly.
