They begin to play, with each man opting to point the gun only at themselves. The intense scene gives Gabriel and Aaron the opportunity to put their respective ministering skills to the test as they extol the virtues of their community in Alexandria, saying, "We're not thieves and murderers. We don't kill each other, we protect each other. Like family."
Mays isn't hearing any of it. He tells Gabriel and Aaron that once upon a time, he was living with his brother and his brother's family, but that came to an end when his brother tried to kill him for the last of their food. After that incident, Mays has come to see humanity as blighted by greed and evil. While Gabriel and Aaron try to convince him to have faith in the idea of family, he tells them that no such concept exists.
Gabriel and Aaron don't give in, though. They continue to express that they not only refuse to turn on each other, but that they also want to give Mays the opportunity to see the light by joining them in Alexandria. Eventually, Mays begins to soften. He stops the game and frees Aaron from his restraints. It seems like he might be ready to join them after all. That is, right up until Gabriel bashes his head in.
Aaron is clearly upset by Gabriel's cynical action. For Gabriel, though, Mays admitted one crucial piece of information that made him incompatible with the mission of Alexandria: He killed his own family. And what they discover next only proves Gabriel's point.