Nygeel:
Well I don't think sex is only a society's construct and doesn't exist outside of society. Indeed there are physical differences between females and males, though the line is a bit blurry.
I had terrarium pets and for some species, it made sense to sex your pets right if you wanted them to survive. For these species, you could say that what makes a man is that the adult males defend their territory against other adult males (while the females have no issue sharing their territory). Also, kids tended to get bullied by adults of both sexes, so you had to put them apart, and they did not always have much tolerance for other species.
For other species (giant millipedes), there were no different gender roles, both behaved the same - no territory issues, no racism (speciesm?) between different giant millipede species, and all lived together in peace & harmony. Only difference was that the males ran after the females for a flirt, not vice versa (and I never saw any gay or lesbian flirts or sex acts in my millipede terrariums). However, if the ladies wanted it too, then they both behaved almost the same during sex and after sex, both were hungry and had a good meal. Only difference was the climax: the guy takes out his sperm package from a pocket, handles it over to the girl and she stuffs it into her pocket. By the way, millipede sex takes several hours, it's very cute, slow and intense and they kiss one another, stroke one another tenderly with their antennae, and cuddle a lot with their hundreds of legs. I want to be a giant millipede in my next life, these are really nice hippie species.

Well as a terrarium aficionado it kind of annoys me if people come to me with this ivory tower theory that sex is a pure society's construct, or gender. When I think about the dramatic iguana war in one terrarium after I sexed one pet wrong, I'm sure there must be at least a bit of this gender role stuff wired in us. Unfortunately, humans are more like iguanas than like millipedes.