I’ll leave you once again with this explanation.
Trans people aren’t claiming anything that is false- they are claiming something about their experience which is very much real.
How are some people autistic? How are some people gay? How does the sun rise in the east? How does time always move forward and never backward? I can’t answer these things, I just know them to be true.
How to some people end up knowing/ understanding themselves to be women/ female, despite not having the right chromosomes or genitals, or social rearing? We don’t exactly know: there’s likely a role for a complex variety of genetic and environmental factors - most likely a role for sex hormone signalling aspects of neurodevelopment. Perhaps an element that is social too. We don’t have all those answers.
What we do know for sure is that some people observed to have male chromosomes in utero , or observed to have male genitals at birth, and registered male, go on to develop the cognitive awareness/ understanding/ knowledge of self as female.
This makes no claims to your experience of being female, or my experience of being female or anyone else’s. it doesn’t mean they are claiming their body, or their feelings, or their personality, or their life privilege is anything akin to yours.
If I say I’m hungry, I don’t know if my experience of needing to eat is the same as yours, I just know that i am hungry.
Trans women know they are female. How and why they know this, we don’t know, but the cognition is what it is- Like hunger. And it’s so visceral , so pervasive , so powerful that repressing/ denying/ contradicting it ,is so disorienting and confusing and nonsensical to the person experiencing it , that it results in profound / acute psychological pain and distress.
it is typically something permanent: unchangeable - most likely because it has a durable developmental underpinning- and not something that can be cured through therapy and attempts to do so have proved very harmful in the past.