... a "gender non-binary person". Change my mind.
Here are the rules of this thread; the requirements in order to change my mind:
[1] You MUST clearly and unambiguously define the term "gender non-binary person" (or "genderqueer person") in a manner that doesn't violate logic and/or science. --- Any and all appeals to HOLY LINKS (e.g, to Wikipedia or to a random dictionary definition) are NOT ALLOWED and will be summarily dismissed on sight.
[2] You MUST clearly and unambiguously describe a "third option" of some sort. Meaning, you must identify and describe:
[2a] A sex other than male or female.
[2b] A sex chromosome other than X or Y.
The floor is yours!
First, you seem to be confusing sex and gender. There are definitely sex chromosome arrangements other than XX and XY. There's XXX and X and XYY, and XXY, and many others.
And there are people who have different sex chromosomes in different cells. Basically, multiple embryos can wind up fusing very early on and forming into a single person who has both XX and XY chromosomes, spread through the body (chimerism). That doesn't just happen with sex chromosomes, either-- it can happen with other genes, as well. When it hits genes impacting skin coloration, people can have odd color patterns in their skin:
https://www.livescience.com/61890-what-is-chimerism-fused-twin.html
And chromosomes aren't the only thing determining biological sex. For example, there are people who are XY yet appear outwardly to be normal women, because they have androgen insensitivity -- meaning their body never responded to the sex hormones that would have caused them to develop male anatomy.
So, even when we're just talking biological sex, it's not a simple binary matter.
What people talk about with gender is different from that, though. It's about which of society's two big gender classifications, men and women, a person more identifies with, if either. It's not about physiology, but rather about psychology. Those who don't feel they identify clearly with either will be said to be non-binary. It's a bit like being asked if you're an extravert or an introvert and feeling neither category really captures your individual situation quite right, and so you reject that binary divide. For some reason, that really distressing some people when it happens in the context of gender.