The parents are judging their children based on outdated, frankly toxic, gender stereotypes, @Daygloboo. There is a set of behaviours, likes, dislikes etc that is in the box marked girl, and a wholly different set in the box marked boy.
So, as @ThatCyanCat says, a boy who plays with a Barbie must really be a girl, because he is exhibiting a behaviour from the girl box. A girl who likes rough-and-tumble games, wears trousers and wants short hair is showing behaviours from the ‘boy’ box, so must be a boy.
Surely it is more progressive to abandon the gender stereotypes and say that biology determines a person's sex, but they can have any likes, dislikes, hobbies, activities, hair style, clothing that they want.
Basically a man/boy is someone of the male sex, with any character, NOT someone with either biological sex but masculine character, and a woman/girl is someone with female biology and any character, NOT someone of either biological sex but a (sweetly) feminine character!