You're missing the point. The child is unable to identify with the body that she has (male body) because her brain identifies her as being female. So she is unable to identify or accept a male body for herself because she is female.
Yes evidently this can and does happen though it be rare. I'm not sure if they know fully why as yet.
No, she's a girl who had the bad luck to be born male.
I identify with my body very strongly. It's the means with which I represent myself to the world. It's the first thing someone notices about me. It better be accurate.
The self has gender and is either male or female?