Absolutely correct.
It's also why birth certificates WHICH ARE A LEGAL RECORD OF A BIRTH AND BELONG TO THE CHILD, not the parent, should reflect biological truth and reality.
I vehemently disagree with being able to change your birth certificate in this instance because of a "gender" identity. I'm NOT talking about cases of DSDs where the sex was incorrectly recorded at birth due to ambiguous genitalia.
If we can "re-assign" or change actual concrete facts, why can't we change the birth date if we feel like it? The occupation of the father or mother? (I want to be an international best selling author and I want the father to be a hospital consultant. While I'm at it I want the birth date changed because I didn't want my baby to be born on a Wednesday. Can we change the birth weight too please, my baby identifies as skinnier than that.)
Birth records are legal documents which capture a true and accurate picture of the circumstances of the birth.
They are not an extension of someone's whims and fancies depending on how they feel or what ideology they currently subscribe to.
Record the FACTS of the birth, not an arbitrary "assigning" of anything.