You aren't necessarily though which is the point. If you medication to regulate your hormones in the way a female's hormones would be regulated, your body largely acts as if it was female. The significant majority of sex related differences from a medical perspective are almost entirely hormone driven.
he exception to this rule are genetic disorders and sex-organ specific health considerations. The genetic disorders are karyotype specific but they aren't sex specific. Likewise sex-organ related issues still apply if you don't have the same chromosomal match-up.
A 46,XX male doesn't have a Y chromosome but they still have all the standard male biology. They have some additional health considerations (mainly infertility) but otherwise they are biologically male and are subject to near identical medical concerns as an average male.
Similarly a 46,XY female has a Y chromosome but they have otherwise physically normal female biology. The caveats being often needing hormone supplements and infertility.
Hell there are even a statistically significant number of people who don't have the same karyotype in all their cells. See 46,XY/45,X0 mosaicism and 46,XX/46,XY mosaicism.
My point being: In every case where the karyotype does not match the phenotypes, the driving characteristics that determines sex in the medical community is the phenotypes/physical expression.
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Now with that out of the way:
Is a man without their sexual organs still a man? Well how do you tell?
- By the chromosomes? Well obviously that doesn't work given the previously mentioned differences between karyotype and phenotype.
- By their sexual organs? Well in this case that doesn't work because they don't have any and/or had them removed.
- By the way they look? There are women who look like men and vice versa and this is quite subjective so it's not an entirely scientific way of making the separation.
- By their hormones? Well this is probably the best one since hormones regulate nearly all expression in the body and with hormone levels typical for a male, the body largely acts male and vice versa. But suppose we don't want to use this. What do we use?
Now do the same for a woman without their sexual organs.
In the end, if you remove the organs the only definitive differentiator between sexes is hormone levels. If you don't want to use hormone levels and you can't use sexual organs, there isn't any other differentiator that cleanly separates between male and female. Every other differentiator has N or 2^N caveats.
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So with respect to trans individuals undergoing sex reassignment surgery, if the differentiating sexual organs are removed/converted (a penis is biologically just an enlarged clitoris) and the hormones are completely replaced to levels equivalent of the sex they are transitioning to, what is left to differentiate them? Doubly so if they decide to transition before or during puberty.
Once again, biology is a lot fuzzier than people seem to realise. There is a lot of grey space and fluidity in sex just like with everything else in biology. The grey space is smaller in humans and mammals in general than in other species but it is well established in the scientific and medical community that sex is fuzzy and can change given the right circumstances.