[Svartalfiar]

There are two sexes and no genders.

That is incorrect. Human biology has two sexes, but there are several species that only have one. Some fungi might even have 3. As for genders, that entirely depends on language. Most have three - masculine, feminine, and neuter. Some have even more, adding animate/inanimate, human/nonhuman, etc. English is one of the few that uses gender very sparingly. The only place I can think of is in some pronouns, which have gender specifically following the sex of their respective noun's subject.

[TigersEye]

What species of clownfish are you?