Why do you struggle with this concept so much? My son is NOT a 'girl living as a boy'. My son is my son regardless of what 'body parts' he possesses or doesn't possess.
One doesn't possess body parts in the way that one possess the coin in her pants pocket. Humans are bodies. Human bodies are sexually dimorphic. If your son's sex is not male then he is a young female living as a boy. Nothing wrong with that at all. Nothing wrong with calling him your son. What is wrong is to pretend that his sex has really changed. Changing one's gender does not change one's sex.
And now we are getting back to the part of the lesson that EVERYONE loves and always kills the thread: your statement is not true.
Here's a hint: the part of their body that does the behaving is not the one dangling between their legs. It's the one seated above and between their shoulders. To continue to pretend that's the bit of their flesh that matters behaviorally is as ridiculous as pretending that it is not the actual hormonal drivers among trans athletes and so as to do your thinking with the flesh BEHIND your legs.
We already see various intersexings of the genitals. What you are proposing is that the actually impactful things re behavior and personality (who someone is!) Is 100% concordant between brain and genitals. Not even genitals are 100% concordant with themselves, re menstruating penises.
And this is not even accounting for the idea that there are most likely various gendered brain regions that can absolutely end up differently configured, and while the apparent differences seem small, this is much the difference between (AND) and (NOT) in a logical system.