Maybe I'm missing something. I have 1 girl and 2 boys. They are distinct personalities, but gender is not a huge factor in who they are or how we choose to raise them. I agree that nature plays a big role, but gender not as much.
There are no guns in our household, but all 3 love laser tag and paintball. Two love math, two love to read, two love art and music, two tell me everything, one I have to pry open. All have a passionate interest in competitive sports. We do nurture some interests better than others, e.g. sports as opposed to music (tone deaf parents), but we try our best. (Except for hockey, one kid tried hockey, liked it, but when it got competitive, I dropped out with teeny tiny bit of regret, kid got over it because basketball was better)
You aren't missing anything - it's not the same in every family. But if you want to see huge gender differences come to my house. I didn't just have b/g twins, I gave birth to a caveman and a princess. Literally. We ARE the stereotype.
My two are learning their ABC's, ds *grunts* them, forcefully demanding in his deepest possible voice that next time won't. you. sing. with. me. grrrrrr!!! He spends his day hunting, fighting and patrolling on his big wheel. DD spends her day gathering, gathering, gathering, storing what she's gathered in purses and backpacks, changing her outfit, checking her look in the mirror and gathering some more. They aren't even 3 yet.
What would men be without women? Scarce, sir, mighty scarce.
My favorite in that department was a gaggle of three old ladies who always sat on the bench outside my supermarket.
When I waddled by, 9 months pregnant, it was,
"Be happy dear. Now is your chance to sleep, because once that baby is born ..."
Baby was born, and I would walk by,
"Be happy, because once that baby starts walking, you won't have a minute of rest!"
Baby started walking,
"You see dear, but enjoy it for now, because you know, soon that baby will start talking and you won't have a moment's peace."
It was normal child development seen as a never-ending succession of calamities. Very sort of uplifting @@.