I think the messages start very early, perhaps more so now than even 20 years ago. Boys are supposed to do stuff, be active, take risks, lead the way. Girls are supposed to be passive, think of others' needs first, tend to their appearance, not to be too uppity of full of themselves.
This idea is reinforced by everything from toys, games, stories and clothing targeting the respective genders, social traditions, family expectations, the media, etc. It's a brave girl that bucks the trend and does things that aren't considered "right" for girls, and they can expect to get alot of flak for it. It's also a brave boy that bucks the trend and does things that aren't considered "right" for girls, and they, too, can expect to get alot of flak for it. If you step too far outside the norm, you can expect not to be popular, perhaps not even be accepted, possibly bullied and not even necessarily supported by trusted adults around you.
I remember it was somewhat like that even when I was a kid in the 70's, but I think now the messages about what is "girl" and what is "boy" are even more pervasive, with the genders even more demarcated than ever before. It's depressing because when you pigeon hole children because of their sex (or class, ethnicity, disability, whatever,) their aspirations and potential are constricted. That's crap for all of us, crap for society.
I don't think it's fair to blame individual girls or boys for not bucking the trend, or insist that there was something inherently "wrong" with the girls in this scenario because they weren't pushing in and being like the boys (or blaming the boys for not being more inclusive and trying to encourage the girls to get involved.)