Atticus thinks that shooting guns is not an appropriate use of his talents. He thinks that it's a talent that gave an unfair advantage over others.

After the incident with the mad dog, Miss Maudie explains to the children: "If your father's anything, he's civilized in his heart. Marksmanship's a gift of God, a talent - - oh, you have to practice to make it perfect, but shootin's different from playing the piano or the like. I think maybe he put his gun down when he realized that God had given him an unfair advantage over most living things."

Atticus, a few chapters later, talks about what true courage is. He is talking about Mrs. Dubose. He says: "I wanted you to see what real courage is, instead of getting the idea that courage is a man with a gun in his hand. it's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do. Mrs. Dubose won ... According to her views, she died beholden to nothing and nobody. She was the bravest person I ever knew."

Not only does Atticus's statement about Mrs. Dubose disabuse the children of any lingering idea that guns are the props of brave men, he also foreshadows his own courageous struggle against injustice in Maycomb, despite being "licked" before he begins.

His choice to never shoot a gun relates to what real courage is, and to being a gentleman who would never take advantage of any living thing.