In humans, behavioral laterality and hemispheric asymmetries are part of a complex biobehavioral system in which genetic factors have been repeatedly proposed as developmental determinants of both phenomena. However, no model solely based on genetic factors has proven conclusive, pushing towards the inclusion of environmental and epigenetic factors into the system. Moreover, it should be pointed out that epigenetic modulation might also account for why certain genes are expressed differently in parents and offspring. Here, we suggest the existence of a sensitive period in early postnatal development, during which the exposure to postural and motor lateral biases, expressed in interactive sensorimotor coordination with the caregiver, canalizes hemispheric lateralization in the “typical” direction. Despite newborns and infants showing their own inherent asymmetries, the canalizing effect of the interactive context owes most to adult caregivers (usually the mother), whose infant-directed lateralized behavior might have been specifically selected for as a population-level trait, functional to confer fitness to offspring. In particular, the case of the left-cradling bias (LCB; i.e., the population-level predisposition of mothers to hold their infants on the left side) represents an instance of behavioral trait exhibiting heritability along the maternal line, although no genetic investigation has been carried out so far. Recent evidence, moreover, seems to suggest that the reduction of this asymmetry is related to several unfavorable conditions, including neurodevelopmental disorders. Future studies are warranted to understand whether and how genetic and epigenetic factors affect the lateralization of early mother-infant interaction and the proneness of the offspring to neurodevelopmental disorders.