Binary mating types are proposed to arise in a three-stage process through selection of nuclear genes to minimize cytoplasmic gene conflict at the time of gamete fusion. In support of this view we argue that: (i) in systems with fusion of gametes, the mating type genes are typically binary and regulate cytoplasmic inheritance; (ii) binary sexes have evolved several times independently associated with fusion, although at least twice binary types have been lost, associated with a loss of fusion; further, in accordance with the theory are findings for isogamous species that (iii) close inbreeding may correlate with less than two sexes and biparental inheritance of cytoplasmic genes; and (iv) species with more than two sexes may have uniparental inheritance of cytoplasmic genes, be rare and be afflicted by deleterious cytoplasmic genes which attempt to pervert normal cytoplasmic genetics. Such facts and their rationale support a new and unified definition of sexes based on the control of the inheritance of cytoplasmic genes. For the common cases, the male sex is that which resigns attempts to contribute cytoplasmic genes to the next generation. We differentiate between sexes and the incompatibility types of ciliates, basidiomycetes, some angiosperms and a few other organisms which are independent of organelle contribution.