I didn't bother with the chromosome argument, because the people making that argument don't understand genetics and in any event, they are using it to deny that people should be able to define their gender and force them into compliance.
You will never be able to understand people who disagree with you on this until you look at your own use of language: you are using the word "gender" as the thing people should be free to choose, but I note you are not using the word "sex". I never hear people say that one can identify as any
sex they want. Why? Because sex has the connotation (now) of meaning physiology, whereas the term 'gender' has been moved laterally to mean something like 'sexualized presentation to others' (yes, it also includes presentation to oneself in a sense). So you can have a term like 'gender roles' whereas we do not speak of 'sex roles' (other than in porn casting I guess). However it was previously common usage to use the terms interchangeably at times, even thought strictly speaking they were not identical. That common usage was almost ubiquitous
except in academic circles such as gender theory, so it should come as no surprise that at first glance there would be pushback on using the word "gender" in a way that divorces it utterly from how it was typically used before. And I don't mean 'in the 1950's' before, I mean very recently. So that's one area of (IMO deliberate) confusion.
Another issue is that our language previously did not have the capacity to distinguish between social agreement and biology. So a statement about one's social presentation (male/female) was always meant to be synonymous with making a statement about their biology. The whole 'chromosome rainbow' thing isn't really a useful reply to this, since the vast majority fit well into the general usage, which is the entire point of general usage. That's why it's ok to call someone you meet part of "homo sapiens" even though strictly speaking many people have a small % of Neanderthal DNA. Now this is not quite an identical case (one being rare cases of discreet differentiation, the other being a more common vague differentiation) but the principle is the same: the language is good enough if it's good enough. We don't need to be more precise in common usage because it doesn't help. On the topic of whether a person should be free (or rather can require others to agree) to choose their own gender this line of argument is truly irrelevant. I know you used it in response to ScottF's proposed XX/XY definition, but while it sounds like a straight rebuttal it's really a red herring. It doesn't contribute much to the discussion where
we are not in fact talking about those people but about 'regular' XX/XY people and how they use language. If the discussion was relegated strictly to those people who do not in fact fit XX/XY then I doubt ScottF would offer any objection.
Bottom line, you are using the word 'gender' in a place where realistically you could but chose not to use the word 'sex'. This is a bit telling, because ScottF is clearly trying to root his position in objective biology, rather than in subjective feelings, and this divide
does seem to be carried across in the contemporary difference between the words 'gender' and 'sex'. Otherwise you'd hear people saying they can identify as either sex, but I don't typically hear that word usage, and I think it's for a reason: because it would imply that you can identify as any biology you want, which makes no sense even to people on the far left. That is why, at least I think, why you don't have people identify as 'black' because that is clearly a genetics issue and it's not really disputable. Yes, there is black culture, and I've even heard some people (not even woke people) say they identify with black culture, but they don't say they "are" black. So the word usage here is part of the axis of disagreement, because many people do not agree that the terms male/female
should refer to social construction elements but rather should be rooted in the biology. So in this context for them it's like being asked to call someone an 'elf' because they identify with elves in Tolkien; it would be viewed as an eccentric and perhaps even rude request to ask everyone you meet to refer to you as an elf rather than a person. Rude in the sense that you're imposing a personal taste onto others' language usage. Not that it would be 'wrong' per se to identify as an elf; ScottF at any rate seems to be saying he doesn't care about that, but that it's about requiring language use (or in the case of some countries potentially,
legally compelled speech). So the disagreement isn't just about whether it's valid to identify as this or that, but whether the common parlance should be pointing to that versus to the simple biology. Obviously this is not a point that is winnable for either side as an argument since it's just conventional usage either way.
What I'm not clear on (or at least it's limited to theories of mine) is why these points seem difficult to see for the gender identification side. It should be pretty apparent what, at minimum, the language dispute is about. Now there are other things at stake, such as social mores, personal comportment, mental health (broadly speaking), and incorrect boxes and lumping people into them, involved, some of which go deeper into the issue. And maybe the surface language disagreement is just a way of almost deliberately avoiding the meatier issues.