An hypothesis is presented by which gamete specialization resolves a conflict between the function and replication of mitochondria. The function of mitochondria is to synthesize ATP by oxidative phosphorylation, which is coupled to respiratory electron transport. This requires a mitochondrial genetic system. However, "incorrect" electron transfers produce free radicals that cause mutation, and the frequency of these events is increased by mutation. Mitochondrial function is therefore detrimental to the fidelity of mitochondrial replication. Damage to somatic mitochondrial DNA may accumulate within, and indeed determine, the life span of individual organisms. Motility of one gamete is required for fertilization, and requires ATP. It is proposed that male gametes maximize energy production for motility by sacrificing mitochondrial DNA to electron transfer and its mutagenic by-products, while female gametes, which are non-motile, repress mitochondrial oxidative phosphorylation, thus protecting mitochondrial DNA for faithful transmission between generations. Male gametes then make no contribution to the mitochondrial genome of the zygote: mitochondria are maternally inherited. This testable hypothesis may help to explain the evolution of separate sexes and a number of their characteristics. Maternal inheritance of chloroplasts may be explained in a similar way, and contribute to the maintenance of separate sexes in plants.