Role Acquisition

Since Maizy has arrived, Alexis and Max have each taken upon new roles. Alexis has proclaimed herself Maizy's second mother. She always wants to hold her, kiss her, rub her head, hold her hand, give her a pacifier, etc. Max has acquired the role of protector. He will protect her toys from others, always asks where she is if he doesn't know, reminds us to put her blanket on, check on her while she is sleeping, etc. It just makes me ponder how this happens. How are these gender roles so innate that at 2 and 4 we already can see them? I mean how does that happen? I might not know these answers, but I do know that Maizy is an insanely lucky girl to have Alexis as a role model and Max as her main man.