I believe nobody is born anything. There is no such thing as a woman born in a man's body. Adults become who they are mainly through their environment gowning up. If the mother is putting ideas on the child of being a female that together with other environmental factors may lead this child to believe so, just how if he is told he is male and should act like a male then he will do so. If he is not pushed either way by the parents(or pushed both ways) then the child will naturally take a stance depending on other environmental factors such as friends, tv shows, school environment, things he has seen or heard etc.....
Our genes broadly dictate how we look and feel,and those genes can make it so that a man feels like he is trapped in a womans body and vice versa.
We all have blueprints before being born and before developing as a fetus that dictate a lot of our lives afterwards,what you say in bolded is black and white and in my opinion nonexistent.