"And it's somehow easier for a girl to cross over into 'boys' territory and play a trumpet than for a boy to take up the flute."Hmm, I wonder why this could be? Perhaps because basically the worst thing to be called/associated with/likened to in our culture is a girl. Gendered insults like "slag", "pussy" and of course, "cunt" demonstrate this. However, it is easier for women to emulate men because there is a general assumption that they are the "norm", and women are somehow deviant from this. Therefore, it actually upholds a patriarchal values system when women express a desire to engage in similar activities to men, because it maintains the assumption that what men do has inherently more worth and value to society, than what women do, which must be regularly derided, and absolutely not emulated.
What is really sad is that children as young as 6 are able to pick up on these cues, and choices which they make are guided by these prejudices.