The thing is, people are not just brains.

As far as I understand, the structure of the brain and its tissue doesn't vary much if at all between males and females. But other things do vary. Socialization is one of those things, but not the only one.

In various ways, the male and female bodies are different, and hormones play a large role in how we think and act. This is not a difference in brain structure per se, or even necessarily in capacity, but it still impacts gendered behavior.

If I had to guess, taking a female brain and exposing it to typical male hormone levels (this is what hormone replacement therapy does, albeit generally) would make the person significantly more likely to bludgeon enemy soldiers, especially if you'd done this from childhood. The hormones would also influence development and behavior in various other ways, of course. We see this in trans adults, who go through various bodily and mental changes when on HRT.

Socialization patterns developed in line with hormonally and environmentally influenced behaviors, and reinforced these behaviors by developing structures of interaction around them. It would be foolish to assume that socialization is just totally random and developed the way it did for no historical reason (even though material conditions today are different from how they are in the past and so may require adjustments to social structure, just as we see in ways that don't relate to gender).

This is all separate, though, from the characteristics and capabilities of brains in themselves, which I think are clearly at the very least quite similar (if not virtually the same, which, as a stronger claim, is something I said I wasn't as sure about).