Gender Inequality

It's certainly worth considering all aspects of socialization, but indeed, it is apparently from the ages of 0-6 where socialization is the most important/ingrained into our subconsciousness. As such, factoring in how parents raise and expose their children to different media (since kids spend the majority of their time with/around parents, as mentioned) is important, but the school can potentially be very important from ages 4ish-6, where kids first look get their experience in the real world, with other people that can affect one's perception (either re-ifying or potentially subverting it) quite a bit, so this could have a particularly poignant impact of seeing girls as leaders/equals in crucial socialization stages outside of the home.

Of course it's not to say people aren't socialized after all this time, we're definitely socialized our whole lives. But both the home and school are both arguable crucially important in socialization.