I would say that Proctor's main motivation is protecting his family and his name. He and his wife know he is guilty of adultery, though no one else does. He hopes the whole hysteria will blow over and he can keep his awful secret, and in waiting so long, the accusations get out of hand. More people are accused, in other words, in part because of his motivation to keep his sin secret.
Later he decides to come forward and put a stop to the madness, or try to, and so this pits him against Abigail. In his desire to save his friends and especially his wife who also stands accused, he confesses, and this threatens Abigail's own life as well, along with that of the girls who went along with her. This makes her more aggressive, defensive and she defiantly sticks to her story.