Usually, if someone says "I am (x)" then (x) is either an objective claim that can be tested ("I'm 39", "I'm 5'5"), or a subjective claim. But even in the case of subjective claims ("I'm a Christian", "I'm a socialist", "I'm angry"), we reserve the right to dispute whether the speaker should be considered a genuine Christian, a true socialist, whether the speaker is genuinely angry, etc. What is odd is to have a claim that is entirely individual-inner-subjective and beyond outside dispute, and then use that inner feeling as the basis for imposing obligations on other people (such as pronoun use).
Language does change, but not usually this quickly. Usually, what changes are the "open" word classes such as verbs, nouns, adjectives. So new nouns come into existence or add additional meanings. Usually, by contrast, a "closed" word class such as pronouns is very slow to change.
You can count me among those of us who didn't get the synthetic/analytic distinction, though I don't think it's essential to the argument:
An analytic proposition, such as “a bachelor is an unmarried man” or “a male is a creature with an XY chromosome pair,” is one whose truth depends wholly upon the meanings of its constituent terms. ... we can know the truth of analytic propositions merely by knowing the meanings of their constituent terms, whereas for synthetic propositions we have to look out into the objective world in order to determine whether or not they are true.
I can't see how you would go about evaluating the truth of “a male is a creature with an XY chromosome pair" without going into the objective world and checking what chromosome pairs males have (especially since the word "male" and its meaning long predate the known science about chromosomes). I believe that males do have XY chromosomes, but only because I've been told that - it isn't something I can work out based on knowing the word "male". I already knew what a male was before I did GCSE biology.