The best evidence that supports the theory that birds and humans have a common ancestor is the presence of vestigial structures. Vestigial structures are organs or anatomical features that have reduced or no function in an organism but are similar to functional organs in closely related species. These structures are remnants of ancestral traits that have been retained throughout evolution. The presence of vestigial structures in both birds and humans suggests a common ancestry, as it indicates a shared evolutionary history where certain traits have become non-functional in both species.