[vehemenz]

Thank you for breaking it down. One objection I might raise in your "given" statements is that the categories we use are not all on equal footing. I think the modern idea of gender identity seems to require dualism—a deeply implausible position—but that's a much longer conversation.

Ultimately I agree that we are making decisions about language. I might break it down differently, as follows.

1. Language about how we identify differences should be useful and effective communicate public facts that are socially salient. Sex is public information and highly salient for courting and reproduction, the basis for most human societies' social organization and primary motivators of behavior.

2. Language about how we identify differences should be self-determined, not based on external facts about the world, and should primarily serve the dignity of the individual. An individual's gender is not society's business, unless they say it is.

If someone has a better formulation of 2, I'd be open. I admit it feels a bit strawman-ish.