A handful of mammalian and avian species can imitate speech (i.e., sounds perceived by humans as those comprising the human communication system of language). Of those species, even fewer are capable of using speech to communicate. While there has been no empirical comparison of nonhuman speech users, parrots are presumed to be the most prolific. In this review, we identify several anatomical, neurological, and sociobiological features shared by parrots and humans that could account for why parrots might emerge as the most advanced nonhuman speech users. Apes and temperate oscine songbirds, due to their phylogenetic similarity to humans and parrots, respectively, are also included in the comparison. We argue that while all four taxa share hemispheric asymmetry of communication areas and basic sociality, humans and parrots share three additional features that are not completely present in apes and songbirds. Specifically, apes, unlike songbirds, parrots, and humans, are not considered vocal learners and do not have sufficient respiratory control to support a speech stream, while parrots, humans, and apes demonstrate complex affiliative social behavior. Along with the above anatomical, neurological, and sociobiological traits, parrots' affiliative long-term relationships, similar to that of humans, may help explain both groups' ability to produce and use a wide variety of sounds. Thus, this paper extends parrot-human cognitive comparisons by introducing another similarity-that of complex affiliative relationships-as a possible explanation for why parrots can produce and use speech to communicate.