Allow me to start 500 million years ago. Our ancestors have been reproducing sexually, with two sexes, for at least that long. Male and female have been real biological categories since then. There are often external indicators—genitals, plumage, song—but the thing that is most fundamental is the type of gametes an individual produces (or did or will or might produce). Females have eggs, which are relatively immobile and large, due to being filled with all of the cellular stuff of life. Males, meanwhile, have sperm (or pollen), which tends to be mobile, and tiny, stripped of almost everything needed for life—except DNA.