Certainly, that is a big part of it. But this should be carefully compared to the "background signal" in these cultures. To take it to an extreme: how certain are you that men go into STEM for reasons different than boys being told "STEM is for boys". Both young boys and young girls have that "common sense" imposed on them by our culture, so it is very unreliable to claim that any choice is unrelated to that cultural experience as a child.