He's an arrogant leader full of self-importance. Think of him as the scrawny little bully who hides behind the muscles of his big bully friend. He thinks himself a right-hand man of Caesar, and therefore very important in the wasteland.
Take Over the Hangdogs: The Prisoner must challenge Bares His Teeth for leadership of the group by pitting his dog against the Packleader's dog. If the Prisoner has tamed the Devil Dog, it may be used for this quest.
If the Prisoner succeeds in taming the wild dog, he will be given a Hangdog warrior name. If the Prisoner managed to succeed in the more difficult task of stealing a puppy from a feral packs lair, it will be turned over to Teacher, and an adult dog will be given to the Prisoner in exchange.
Before the Hangdogs were merged with the Blackfoot tribe, Bares would have had no qualms about banishing Sharptooth and his family for Sharptooth being a Legion spy. Bares would have also joined the Hangdog rebellion if the Prisoner had become leader of the tribe and showed mercy to Sharptooth.