They're Taught That Their Job Is To Please Other People
Our school system is designed to reward children who obey, because when a teacher tells a child to get in line, we need them to say "OK," and not "It's all love, but I'm going to follow my own truth and try to crawl out this window instead." But it seems like there's less tolerance for girls who rebel than boys, as if the latter are expected to be back-talking scamps every now and then. Girls, meanwhile, are all supposed to be sensible Hermiones.
That's at least partly because we're trained to be caregivers. Sure, you might find a pink dirtbike in the girls toy section, but there are still going to be a lot more kitchen sets and toy sewing machines. I once had a beloved toy vacuum. All the fun of real vacuuming -- which is to say, none!
Socializing girls to be caregivers, to cook and clean and raise plastic baby dolls to grow into plastic disappointing adults, means teaching them to care what other people think. There's less room to mess up because, it's implied, the stakes are higher. Everyone is depending on you!