Yes, we know a lot about what children are exposed to. It's been studied for decades in depth. You have not raised your kids neutrally because there is no way to do that unless you lock them in the house and they never meet anyone else and never read any books or watch any tv.
"Constant exposure to dated concepts of gender roles and norms in the media starts before preschool and continues from there — concepts like: Boys are smarter than girls; certain jobs are best for men and others for women; and even that girls are responsible for their own sexual assaults. This was the finding of the 2017 Common Sense Media report Watching Gender: How Stereotypes in Movies and on TV Impact Kids’ Development."
The other thing that's been studied for over 40 years in depth is how the Man Box impacts men. Of course, not everything is socialization - but it does exert a powerful impact and pretending it doesn't is just bollocks.
And I didn't say that men and women are the same. I said that all people are individuals and those differences get expressed through their gender. Pretending like RuPaul and Donald Trump and PeeWee Herman have a lot in common because they are all men is just preposterous. And there are women out there who can bench more than you, who are way better at math than you, who are more logical than you, etc., etc. How can that be in a binary system?
Your thesis about heterosexuality just doesn't make sense or hold water. What matters for evolutionary success is diversity - not a binary homogeneity that need to complete each other somehow other than through joining their genetic material via their complimentary genitals - but that's kind of where it ends - with the genitals. And aside from the fact that your theory doesn't really make sense because until 40 years ago we did need complimentary genitals to procreate, we can see with our own eyes how mating doesn't actually occur in the world in the way you are describing. Expert after expert on human sexuality has pointed out that there is no one single mating strategy employed by humans. It's highly dependent on a wide variety of things - one of which is socialization and culture, but also things like environment and other elements.
And for humans sex is about more than procreation. You can't just reduce it down to that. Things like attraction and love are just a lot more ineffable. Men and women may be different in some kind of fundamental way, but we have yet to discover what that is because there are too many exceptions to every single rule and norm - and there are differences from culture to culture and time period to time period. The Mosuo of China are a matrilineal culture. The women do all the farm work and other heavy lifting -other than the building of houses, which the men do. Women are the head of households, and boys and men do a lot of caring for the children who live in the household of their mother or grandmother (where everyone lives).
"The matriarchs (photographer Karolin) Klüppel met were “often very funny, and very active”, at odds with the German culture she is used to. “I saw an 80-year-old women carrying things I could no way carry myself,” she says. “Their bodies are really tense with power. I realized that physical strength really depends on what you do with your body — the women have more strength than the men!” ~National Geographic
So, how exactly does that fit in with your thesis?