Gut microbiomes of humans carry a complex symbiotic assemblage of microorganisms. As in all mammals, the special mode of feeding newborn infants through milk from the mammary gland enhances the opportunity for vertical transmission of elements of this microbiome. This has potential benefits, but it also brings with it some hazards for the host. We point out here that vertical transmission from both parents would allow host populations to be invaded by elements that are deleterious. In contrast, vertical transmission, when restricted to one parent, acts as a sieve preventing the spread of such elements. Because some transmission from mother to infant is unavoidable in placental mammals, uniparental transmission of symbionts, if it were to be selected, would require some separation of the father from the newborn infant. This paper therefore puts forward the hypothesis that the asymmetry in roles of mother and father, together with the hazards that come with biparental transmission, generate a selection pressure against male lactation in humans, and in mammals in general.