The disagreement isn’t over the physical facts; it’s over how "sex" should be defined, recognised and applied in different social, legal and scientific contexts.
Interesting.
So, taking it from your perspective, they are aware of their bodies and have discomfort/distress about it. In the vast majority of cases their body is healthy and features are within the normal ranges, but they think the words are wrong.
How does that form a reasonable basis for redefining words such as 'sex'?
Why would a child's perspective on this be taken as a reason to change the word meaning altogether?
If redefining the meaning of sex to accommodate them is important, how does it then naturally follow that their body must be altered?
Bringing us back to the question of how does this justify giving puberty blockers to children for transition?
Alongside that, I think we may ultimately need new terminology altogether.
I would agree. And for more than just 'gender'.
Although, as you have pointed out, a large part of this is about redefining words. Gender, sex, man, woman, he, she, male, female.
You appear to be trying to find a measurable biological reason for transgenderism that can form the basis of redefining the meanings of these words. This idea is rejected by a lot of trans people and allies, including clinicians.
I think it's an area worthy of study, before a puberty blocker trial is considered. So far investigations have found nothing conclusive.