What causes Jem and Scout to see their father with a new perspective?

Scout doesn't think her father can "do" anything besides be a lawyer - he doesn't do hands-on physical work and he doesn't play football. He's much older than the parents of her peers, which makes it difficult for him to take part in such activities. In addition, Atticus wears glasses because he's nearly blind in one eye. Instead of hunting, he sits and reads inside. Scout is slightly ashamed of her father, because it seems like he can't do anything noteworthy. Atticus tells Scout and Jem they can shoot their air guns at tins cans and bluebirds, but that it is a sin to kill a mockingbird. Miss Maudie affirms this, saying to Scout, "Your father's right. Mockingbirds don't do one thing but make music for us to enjoy. They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird."

One day a dog named Tim Johnson appears in the neighborhood, down the street from the Finch house. He looks strange appearance and walks slowly, with a twitch. The children tell Calpurnia, who takes one look at the dog and immediately calls Atticus to tell him that there's a rabid dog in the neighborhood. Next Calpurnia gets the town operator to call everyone in the neighborhood to warn them. She even runs over to the Radley house and yells a warning to them. Atticus and the sheriff, Heck Tate, drive up, and the sheriff gives Atticus the gun. The dog is so close to the Radley house that a stray bullet might go into the building. Atticus reluctantly takes aim and shoots the dog. The dog crumples into a heap. Jem is dumbstruck with the accuracy of his father's shot. Miss Maudie tells the children that their father used to be known as "One-Shot Finch," the best dead-shot in the county. She says he doesn't shoot unless he has to, because he feels that when he holds a gun, God has given him an unfair advantage over living beings. Scout wants to tell everyone in school about the incident, but Jem tells her not to. Jem explains that he wouldn't care if Atticus "couldn't do a blessed thing," because Atticus is a gentleman.