Apologies for attributing ideas to you that aren't yours.
You can't recognize yourself as a girl unless you have some kind of mental model of what a "girl" actually is. I didn't ask "what is it that makes you think you're a girl." I asked "what is* a girl, to you?"
I'm asking about the meaning of the word "girl". The answer is not a list of attributes. But it means something, to the boy who claims to be one. What does it mean?*
I think you're still making an assumptions about how human cognition works that aren't justified.
Of course a child needs to have acquired some understanding of the words "boy" and "girl" to use them meaningfully. But that doesn't mean the concepts themselves produce the child's identification with one category rather than the other. That identification may arise from underlying neurocognitive processes, while socially acquired concepts provide the means through which the child comes to understand and describe it.
Take something as apparently simple as knowing that your arm belongs to your body. How do you know it's yours? Is it because you can see it? Because you can feel it? Because you understand what an arm is and have consciously concluded that this particular arm belongs to you?
Neuroscience tells us that bodily self-recognition involves complex processes operating largely outside conscious awareness.
For example, there's a fascinating neurological condition called somatoparaphrenia, in which people fail to recognise one of their own limbs as belonging to them. Some patients can see their arm, experience physical sensations when it's touched, and understand perfectly well what an arm is, yet still insist that the arm belongs to somebody else.
Their problem isn't that they don't understand the meaning of the word "arm", or that they've incorrectly reasoned about its characteristics. It's that the neurological processes involved in recognising the limb as their own have been disrupted.
Now, I'm not suggesting that gender identity and bodily ownership are the same neurological phenomenon. We don't know that. But this illustrates an important principle: our recognition of ourselves isn't necessarily produced by consciously evaluating characteristics and deciding what they mean. The brain can generate that recognition through underlying cognitive processes that we can't directly access or explain.
So, when a child says "I'm a girl", of course we can ask what the word "girl" means to them. We can explore their understanding of sex, anatomy, social expectations and gender stereotypes. Those are all legitimate questions.
But the child's answers tell us about their conceptual understanding of the category. They don't necessarily explain the cognitive processes through which they came to identify with it.
My suggestion is that our capacity to recognise ourselves in relation to sex categories is influenced by underlying neurodevelopmental processes. Language and social learning provide the concepts through which that recognition can be understood and expressed, but the neurocognitive processes underlying the identification may themselves be rooted in the brain's underlying organisation, rather than simply acquired through social learning..