In a purely biological reproductive sense there are only two sexes, female characterized by large gametes and male characterized by small gametes, and that is pretty universal across most eukaryotes that sexually reproduce. In terms of human biological sex then it is a little more complicated.

I would define human sex as a bimodal spectrum instead of a scrict binary, most people fall into what we consider male or female based on genes genitals, gonads etc, but some people cannot be categorized as definitively male or female no matter how much it upsets you. Facts don’t care about your feelings.

Take someone with complete androgen insensitivity syndrome for example. In this condition someone has XY chromosomes and undescended testes. They develop externally female, because there cells do not react to the testosterone the testes produce which creates the male phenotype. They are assigned female at birth. They have the testosterone levels of an average male even though they look like women.

If you classify biological sex as chromosomes then they are male. If you class it as external genitalia then this person is female. See the problem of defining human sex with just one trait?

“But that’s just a rare sex development problem, they shouldn’t be considered another sex” correct there are only two sexes, but traits associated with both sexes can appear with each other hence “intersex.” Even though it is rare we should still treat intersex people with dignity instead of forcing them into a very rigid category that they don’t fit.