The investigation of human cognition benefits from a dual perspective approach, as the evolution and development of modern human abilities are inextricably linked. It is widely acknowledged that humans demonstrate population-level right-handedness, linked with dominant left hemisphere control of language processes. Additionally, it is recognized that a significant majority of mothers cradle their infants with their heads resting on the left arm, associated with a right hemisphere dominance for social-emotional processing. Yet, in both cases, species-unique, causal relationships are debated. The following presentation focuses on behavioural evidence from human and non-human animals supporting a theoretical supposition that evolutionarily old left and right hemisphere dominances for primitive survival behaviours provided a platform for the evolution and development of sophisticated communication and social-emotional abilities in modern humans. Moreover, it is hypothesised that primitive cerebral dominances still play a critical role in the typical development of cognition in children.