I believe parents hobble their daughters by not supporting intellectual activities that are out of the norm. This is why there are so few girls in the science field though that is changing in recent years. I think most parents are more likely to support a son that has a talent for chess then a daughter.
And no chess is not manly but I think the social stigma of little girls growing up to be mommies and housewifes or other less intellectual pursues still plagues our society.
The theory that parents discourage their girl children from intellectual pursuits sounds completely bogus. Certainly not in the United States in the 21st century.
Girls get better grades in school than boys. If parents were encouraging boys to be intellectual and not girls, we'd see the opposite pattern.
Girls are also more likely to attend college than boys. Once again, more evidence that there's no parental discrimination against girls.
Once again, I point out that supposedly-masculine mental activities such as science, math, computer programming, and chess, are not inherently masculine. They don't require big muscles. Boys who do well at these subjects are not even though of very highly, they are thought of as nerds and not cool. If anything, there's more stigma against boys who do these things than there is against girls.
Why can't you just accept the obvious, that girls' mental talents are, on average, not as chess-oriented as boys'?
why should we assume that on average male and female brains process chess identically?"
I don't think anyone holds that assumption. I think a more pertinent question might be that if men and women do process (chess) information differently, does that difference matter? Maybe it does... or maybe it doesn't.
"I think that statistically, men and women have marked differences in their aptitudes "
I think this is true when such aptitudes are measured later in life but less true when measured in children. I beleive you'll discover that at the elementary school level, girls on the average show an aptitude for chess at least equal to that of boys. Since aptitude is generally considered something hard-wired into us, I would think that it would be evident in any age level, but it seems that girls on the average tend to become comparatively less apt the older they get.