Reminds me of similar arguments about the word "atheism." Etymologically, it means: lack of belief in God. It contains the word "God" in it. So, in a debate about whether God exists, theists often smugly note that they have the upper hand in the debate because atheists have (supposedly!) conceded the centrality of God in their own self-label. The whole debate is already about God: arguments pro, arguments con. There is some validity to this observation—I mean, the theists have framed the debate. They are the ones making the more outlandish claim about an invisible, all-powerful being, and the "atheists" are whoever responds "no" to their claim. Regular people aren't labeled "atheists" or "unbelievers" until they are provided with a specific supernatural claim to not-believe in. So, yes, the word "atheism" is an acknowledgment of how the debate is framed, but that's more an acknowledgment of power dynamics rather than of evidence that God actually exists. (The fundamentalist retort "but how could you talk about 'God' if there were no God?!" is of course irritating nonsense. How could you talk about the nonexistence of "fairies" if the word "fairy" didn't describe something real after all? Why is the word "fairy" in the dictionary if fairies aren't real? Really. )
Anyway, your comment here is applicable to that. Belief in God is the "spawn point" for debates about theism/atheism. Atheism should be taken seriously, but everyone also needs to acknowledge that atheism does, in some sense, owe its existence to theism. That's not a critique of atheism. The atheist may be factually correct, and the theist may be factually incorrect. It's just that the theist has opened the inquiry in a particular way, so the inquiry is named after their position. The theist is like the person who opened the court case. They are the plaintiff, so the court case is named after them, and the defendant has to respond to the specific thing they are saying. That doesn't mean that the plaintiff's framing has merit.
If I understand you correctly, you are saying something similar about gender. The world goes around saying "Gender binary! Gender binary!" and the nonbinary person responds "No" (hence their label). That label describes the argument (as illustrated simplistically in the previous sentence) but doesn't adequately describe the whole person and how they live. The person does other things with their life and thought besides saying "no" to an existing gender system they find invalid. "Nonbinary" is one thing that they indeed are, at least in one context: They are nonbinary insofar as they are saying "no" to a binary. But they might also want to describe themselves positively (without the use of "no" or "non") in terms of what they do feel and believe. Maybe they are, for example, an egalitarian, a libertarian, or an anti-colonialist, and (within those philosophies, in their view) there may indeed be a gender-free assumption or the lack of any assumption about gender, but those labels (egalitarian, libertarian, anti-colonialist) also mean something beyond what those philosophies are or aren't saying about the existence of a gender binary. Maybe when the gender binary isn't picking an argument, certain people don't pick an argument with the binary, and those people believe various things about the world for other reasons (because their lives are not wholly dedicated to arguing about a foundationless binary, as important as it is to challenge that specific oppression), and they would have to tell you what those other things are. We could ask whether and how their other beliefs also resist the gender binary, but then we are the ones who reintroduce the "nonbinary" framing.
