We seem to be going in circles and revisiting the same argument from a few pages back. I'll try to be a bit more succinct.
The issue with your position is that it stems from a weak premise:
If something/someone A looks like something/someone B, something/someone A objectively is something/someone B.
This is a weak premise because it will not always lead to an objectively true conclusion when applied universally.
For example:
Rachel Dolezal looks like a fair-skinned Black woman. Therefore, Rachel Dolezal objectively is a fair-skinned Black woman.
The above argument does not reach an objectively true conclusion due to its weak premise.
The same applies when it comes to the matter of identity. The issue is that the term 'identity' itself has been conflated to mean
what someone is, as opposed to its correct definition which is
who someone is.
Identity is 100% a sociocultural component of being human because it is malleable and is a very unique and personal aspect of each individual person. It is not measurable. It exists within the
subjective space (i.e things that can be changed and are not measurable). Therefore, the concept of identity cannot be applied to that which exists within an
objective space (i.e. things that cannot be changed and are measurable).
DNA and genetics are aspects of biology that cannot be changed. Biological sex is coded into an organism's DNA. Taxonomical components are coded into an organism's DNA (i.e. species). Age is also expressed in one's DNA and can actually be determined/measured through epigenetics.
If an organism is part of the human species, female, and a child, that human is not a woman. That's a girl. The girl will become a woman once the adult life stage is reached. If that woman changes her phenotype to look like a man, that woman does not objectively become a man. The woman remains a woman who now
looks like a man.
Do keep in mind that it is not always necessary to medically change one's phenotype to look male or female. There are social and cultural factors that standardize phenotype, as well (i.e. masculine and feminine).
A form of this is colloquially known as cross-dressing and has been used as comic relief in many forms of entertainment as I'm sure you're aware.