> You either produce sperm, or ova - or neither (which if caused genetically is an abnormal variant).

Or both, at least in theory, though true hermaphroditism with both ovulation and spermatogenesis, while theoretically possible and observed on other mammals has not, AFAIK, been conclusively shown in humans.

But, sure, you can redefine “sex” to be restricted to any one of a number of axes of sexual variation that exist in human and result in either a simple quaternary, trinary (or, if you try a little harder than you have, binary) distinction, but what is the point?