When we teach children a novel word by pointing to an object, we expect them not only to become able to say the word when they see the object again, but also to become able to remember the object just by hearing the word. Inferring the new relation “if you hear the NAME then remember the OBJECT” based on the learned relation “if you see the OBJECT then say the NAME” is called symmetry and it has been reported that non-human animals rarely show this ability. However the matching-to-sample procedures used to examine whether non-human animals have this ability seem to have problems as a method to test the above-mentioned ability that is involved in learning and using words. Still, human adults show symmetry even when tested by using such a problematic procedure, whereas human infants rarely show symmetry in this task. Based on these facts, the relationship between language use and the emergence of symmetry was discussed.