In random mating populations, the fate of mitochondrial mutations with sexually antagonistic effects in males and females is based solely on their effects in females. Therefore, mitochondrial mutations that are beneficial for females but deleterious for males will be fixed in a deterministic model. Why then are males not less fertile? One among many several explanations is that inbreeding limits the ability of mutants to spread since the fitness of a mother is now linked to her son's fertility. We model this situation analytically and determine conditions under which such sexually antagonistic mitochondrial mutants can spread and fix in a population. We also provide alternative hypotheses for the lack of observed male sterility in natural populations.