I'll try again.
A person's gender identity is simply their recognition/ awareness of self in relation to sex categories "male" "female" "girl" "boy".
You are still stuck in this loop of assuming that when a child says "I'm a girl" - they are arriving at that conclusion by comparing themselves to a set of "meanings" attached to the category "girl". "I am a girl because I wear dresses and girls like dresses", "I am a girl because I like pink and girls like pink." "I am a girl because girl's have a vulva and I have a vulva", and so on.
But there is no evidence that gender identity works like that.
In fact, classic cognitive-developmental theories distinguish children's basic identification with a gender category from their knowledge of the stereotypes and characteristics associated with that category. They propose that developing gender identification itself motivates children to explore what being a boy or girl means socially.
You tell me you don't even have a gender identity! When I point out to you that you do because you recognise/ are aware of your sex, you tell me that's rubbish! That's not a gender identity, you just know you are a woman because you have xx chromosomes and a vagina. But gender ID typically develops before that knowledge.
When I asked my four your old, "how do you know you are a girl?" She wasn't able to articulate any reason, any "meaning" all. She continues to reply simply "because I know that I am".
She doesn't know she has xx chromosomes and that means she's a girl. She didn't say "I'm a girl because I have a vulva", she didn't say "I'm a girl because I wear dresses". So how does she know she's a girl?
You might say it's because I told her she's a girl and that may well be. But the important point is that her identification doesn't appear to depend on consciously comparing herself with a list of characteristics associated with girls. She simply recognises herself as a girl.
And if gender identification were simply a matter of internalising the category assigned to us by others, how do we explain children who have consistently been told they're boys, yet persistently and insistently identify as girls?
Your answer seems to be that they must have learned some beliefs or stereotypes about girls and mistakenly concluded that those characteristics apply to them.
But why must that be the explanation? It's one possible hypothesis, certainly, but you haven't provided evidence that it's the correct one. You can't establish it simply by insisting that no other explanation makes sense to you.
Another possibility is that our capacity to recognise ourselves in relation to sex categories is influenced by underlying neurodevelopmental processes in the brain. These might interact with social learning, which provides the language and concepts through which that recognition becomes possible.
Have to run!!