Now, let's assume some people indeed are born in the wrong body

But why assume this even for the sake of argument? How on earth can someone be born in the wrong body?

This daft idea of being born in the wrong body only make sense to those who have no clue about how human conception occurs and what happens afterwards during implantation in the uterine wall, followed by all the various stages of embryonic and fetal development over the next 40 weeks, followed by all the millions of things that happen during the long course of infant and child development, puberty and adolescence. How babies are made and what happens to infants, children and adolescents as they grow into adulthood are not mysteries. It's all been well studied and well documented.

The human brain, neurological system and reproductive organs develop along with all the rest of the body. Development of brain, mind and body are all of a piece. Coz we are our bodies. We don't exist as disembodied minds apart from our bodies. And every one of the cells in our bodies from the time we are conceived until after we die contains our sex chromosomes. If we are buried and our bones are dug up centuries later, our sex will be still be clear from the shape of the pelvis and our DNA.