People are heavily influenced by their environment and media. Imagine that you grew up alone in an island empty of humans or 200 thousand years ago or on another planet. Your aspirations would not contain almost all of what they contain when you are here in this time and place. These stereotypes when children are faced and bombarded with all the time they affect the children and create references in their minds of these images and suggestions. These images and the environment in general that children live in shape who these children are going to become like when they grow up. It forms who they are. These children then start to imagine life as just that and start believing this is all there is. It is still allowed and legal to be a dancer female, but this should not take a bigger preference over being a female engineer just because you are born a female and as a girl you should pick up some girly career.
There are some girls that are “girly”. There are also girls (like myself) that aren’t very “girly”. All sides should be shown, the pink-wearing girl that loves playing with dolls, the metal girl that wants to be a knight or a ninja when she grows up, and the science-loving girl who’s always reading physics books. They all exist and that’s good, because mankind can flourish in diversity.