larry - I don't agree with you on much else, but your thinking on this subject is not far from mine.
" I think gender is based on biology and reinforced socially"
Some of it, yes. Women are physically weaker than men and give birth to the babies, so it is not hard to understand that they have been relegated to the traditional homemaking/child rearing roles while men have been the hunters. With these roles have come vast differences in power and authority, with which gender roles are further reinforced by the powerful class - men are accepted to be not just physically stronger but also more able in whatever they do, even in management positions that require no physical strength. Women are not listened to as much and are raised to be sweet, told not to argue, etc.
So yes, there are biological differences between men and women that are the basis for gender roles, but the whole story woven around those roles such as girls like pink & dressing up being pretty, boys like intellectual stuff etc are still bullshit.
"an operations X hormone treatment repressing a substantial degree of the biological expression of the Y chromosome (the testosterone),... the resulting person was far closer to a woman than a man. "
The resulting person is still a man (= adult human male, where male = of the sex that can make sperm and not eggs) who appears to be closer to a woman than a man.
It is very VERY important to be able to distinguish between what looks like and what is. A male who no longer looks masculine without facial hair and with breasts is still male (i.e. of the sex that can make sperm) and will never be female (i.e. of the sex that can bear young or make eggs).
"And if they want to be considered a woman, what is wrong with that?"
Nothing on an individual basis, but again "considered as" is not the same thing as "is". I have no problem considering my TM friend a man, but we both know that my friend only looks somewhat like a man and is not a man - doesn't have the necessary Y chromosome or the organs, will never have any physical function associated with being male, a fact reminded by yearly smear tests.
On a population level, accepting all TW as women has devastating consequences for half the population, in subjects ranging from safe spaces, medical treatments, sports, statistics, and prisons, to name just a few. All have extensively been explored on these threads so you will all know what I am talking about here.