Assigning instruments to boys vs. girls is a cultural construct. It's easy to test. Just look around at other cultures. Do children all over the world think the same thing? The answer is no. In some cultures, men play flutes, women drum.

But the social pressure in this culture can be intense. When I was in school, I knew several boys who wanted to play the flute. They didn't dare, though. They'd get beat up every day if they did. Not one single boy played the flute in my school band.

Some did play clarinet, but it was iffy. They got called fags regularly. Woodwind instruments were for girls. Except the saxophone. That was a boy's instrument.

Gender roles can be random - men play vertical flutes, women play horizontal flutes, say, or men wear skirts, women wear pants. But often, there are solid economic reasons behind gender roles. A group under population pressure will generally value men over women. Control of females is control of fertility. You see this writ large in China. Their one-child policy has resulted in a high rate of female infanticide. (And how better to justify infanticide than the belief that women are inferior, less human?) It will certainly solve their population problem, when millions of boys grow up and find no wives available.

In a society that is not under population pressure, where a woman can raise children without help from a man, that is generally what happens. Society is built around related females and their children, with the men wandering in and out at the edges. (I think that is where Western cultures are headed now.)

Perhaps the most well-known case of this are the Mosuo, at Luo Lake in China. Women do everything. They make all the decisions, do all the work, own all the property, pass their names to their children. Most do not get married. They practice something called "walking marriage." A woman will tickle the palm of a man she likes, and he will be expected to show up at her house that night. They will sleep together, but he's expected to be gone by morning. The woman keeps any child of the union, and raises it with the help of her mother and siblings. I read an interview with one Mosuo woman who had married an American and moved to San Francisco. The marriage only lasted two years. The woman was raised to be in charge, and could not get used to American gender roles.