There's no circularity in saying "reproduction in humans occurs by the fusion of two differently sized gametes; the producers of these different gametes are defined as the sexes".

You're confusing "how sexual characteristics look on the surface" with "what sex someone is". We *don't* define sex as "what chromosomes you have". Yes, usually XY and XX are sufficient to define your sex--ie what gametes your body is organised to produce--but not always. There's a fascinating paper online of a Croatian woman (who had a healthy female child) who is XY plus some XX mosaicism. That's because her Y chromosome has a non-active SRY gene, plus other stuff going on. Nobody sensible would say she's a man. Nor that she's trans. She's female: an egg producer. (This is also why biologists do not define sex by chromosomes, but by outcomes.)

Chromosomal abnormalities such as XXY (male; Klinefelter syndrome) and XYY (male; Jacobs syndrome) just show that meiosis isn't perfect. (There are other DSDs which arise at other stages of development.)

These don't mean that people aren't one or the other *sex*, even if they *appear* somewhere between. You need to discern between the underlying sex, and the presentation. Everyone *is* one sex or the other, and the primitive sex-drive part of our brain tries to identify everyone we encounter as one or the other sex (because our hindbrain wants to know if we can reproduce with them or not). There's no spectrum there. But everyone can *present* how they like. That's where the "spectrum" arises.