TheMonkeyMummy Not inflammatory at all, thank you for being kind about asking!
I never mind being asked with genuine curiousity, I am no expert but I have learned a lot along the way & am still learning.
Your Dad said what a lot of people ( probably even me once ) think.
The way I look at it, having spoken to lots of trans kids & some adults, is this.
Regardless of what labels are put upon us at birth or throughout life, if what you feel inside is so strongly different to the outer presentation then by transitioning you are not changing your gender merely realigning the outer self to match the inner self. We prefer to say gender realignment rather than "sex- change" for example, a more positive phrase .
Trans children will often say they don't want to change what they ARE, but the outer shell that doesn't match. It goes beyond clothes, toys or gender stereotyping, its the strong sense of self.
My child is still the goofy, cheeky, gorgeous being he always was, just not in the form I thought he was meant to be.
HTH just rambling a bt really it is difficult to explain, its such a personal thing to go through & each child & family is unique although with common ground.
I'll see if I can find something more concrete to point you towards.