Researchers studying symmetry, one of the requirements for establishing stimulus equivalence, have contrasted inferences made by human and nonhuman animals and suggested that inference in each animal species is determined by several biological factors developed in the course of the evolution of a given species. This paper reviews the relevant experimental studies with human and nonhuman animals, including studies of young children, individuals with developmental disabilities, and nonhuman mammals. This work indicates that developmental, ethological, and behavioral factors are closely related to produce symmetry. In searching for the neural factors of symmetry, evidence from fMRI studies suggests that brain activity associated with equivalence relationships occurs in the processing of stimuli with or without temporal order. Thus, further research on the processing of temporal-spatial factors of stimuli is needed in both human and nonhuman animals. A detailed analysis of human subjects failing to establish equivalence relationships, and of nonhuman animals performing prerequisites for symmetry, such as identity matching and matching by exclusion, is crucial for understanding the biological origins of symmetry inferences.