My sons Nico and Leo (now aged 12 and 10) recently had a conversation that illustrates what they've learned about gender.
As background, keep in mind that the kids have never played the game "Portal Gun" but they have watched videos on YouTube of people playing the game all the way to the end, plus YouTube has taught them lots of songs about the characters and stories from "Portal Gun." (This is one of the bizarre aspects of our Internet age that I never would have predicted...)
Anyway, unlike most first-person shooter games, the first-person character playing the game is female ("Shel") as is the main villain ("Glados" -- the computer that runs the Aperture Science Center).
Nico: I guess Portal Gun shows that girls can do anything boys can do.
Leo: Yeah, but boys will never believe it because boys are too selfish! Ha, ha boys are too selfish to believe it! [pauses to think] Of course, girls are selfish, too. Everybody's selfish.
I just chuckled and didn't make any remark. But, naturally, a lot of things jumped out at me from this tiny exchange.
First, it's clear that they've picked up certain gender-privileged assumptions. The fact that a male protagonist can set off on a video game adventure goes without saying. A female protagonist on a video game adventure is strange and noteworthy -- something to glean a lesson from. And you can see that my kids are using their brains, making an effort to find and learn those lessons that are out there to be learned.
Second, I want to make it clear that I never told them "boys are selfish" or taught them any other such lesson. Leo has concluded that it is very bad to be selfish, and will often remark on whether various behaviors are selfish. To be honest, I'm not entirely sure where he picked up his rejection of selfishness -- I'm ashamed to admit that I've been pretty lax about formally teaching my kids ethics -- but I'm not complaining.
Third -- and I'm probably reading too much into this, but -- I think Leo shows some pretty good empathy there for a 10-year-old kid. Neither boys nor girls are inherently better nor fundamentally different from one another. But this same human nature, given different circumstances and experiences, can manifest differently.
Also note, I'm currently reading them the "Little House" series as their bedtime story (I've also read them Heidi and the entire Harry Potter series, among other things), and Leo loved the "Dora the Explorer" stories. So, while having a female protagonists in a video game is noteworthy, reading stories with female protagonists isn't.
I think this shows some kind of progress. I remember when I was a kid that there was some common wisdom that for a story to appeal to both boys and girls, the protagonist has to be male. OK, actually I think people still believe that. (When I told my German teacher that I was reading my boys "Heidi" she protested that the story is for girls...) But experience shows it's not true.
Come to think of it, I don't think I've read them "Alice in Wonderland" yet...