So why would any atheist every do anything good, in private?
One or both of those reasons. It's a fact of human nature, even among the insane. Whether it's that it pleases him to have felt that he's done what he guesses is "good," because it affirms his self-image; because it gives him some advantage; because it helps society (which makes him feel good).
All behavior is motivated by desire for reward and/or fear of punishment.
Dan
Self satisfaction.