I am not sure that just because someone produces sperm vs eggs delineates them as male vs female. You could produce sperm but have endocrinological phenotypes (driven by genes) affect your physiology, so it wouldn’t make sense to keep insisting that one is male then.

Also, how does this definition take into account intersex people who produce both types of eggs? They’re a man? Or woman? What subcriteria would you use to define them, and then why wouldn’t you use that same subcriteria on single-cell producers?

At a socio-political and cultural level, it seems useless to worry about how someone’s sex is defined. There’s no purpose served other than to create a class of people who can conveniently be othered and used as a means to distract from people who are truly damaging to society—the greedy and resource hoarders.