Explain the significance of Atticus shooting the mad dog, Tim Johnson, in To Kill a Mockingbird.
In this chapter, Atticus very reluctantly kills a rabid dog, Tim Johnson, with one shot. He doesn't want to do it, but rises to the circumstance. As a result of this incident, Scout and Jem learn that their father was once an expert marksman. They admire him more than they did before, because they recognize being a good gunman is a talent the rest of the community considers manly, brave, and admirable.
However, the real lesson they learn is that Atticus has his own moral compass, separate from that of the larger community. He doesn't like to kill things, especially with a gun, as he shoots so well that it gives him almost total control over other living creatures. He doesn't want to take advantage of his power. And just because the community approves of it, doesn't mean he is going to brag about his marksmanship or use it as way to raise his own esteem in their eyes. This way of living offers insights into his defense of Tom Robinson.
The children learn that one can both live in a community as a part of it and hold to one's own moral standards. As Jem says at the end of the chapter, his father is a real gentleman—gentleman in both senses of the word: a polite, dignified man of a certain social class, but also a genuinely gentle man. Or as Miss Maudie puts it to the children, he is "civilized." The children learn from their father's example and Miss Maudie's words that being civilized means not taking advantage of what you have to hurt others:
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. I guess he decided he wouldn’t shoot till he had to, and he had to today.
In addition to recognizing that their father was not "feeble," inadequate and unmanly, the killing of the mad dog served to teach Jem and Scout the definition of humility. Jem wonders aloud why Atticus had never told them about his marksmanship skills, thinking that "he'd be proud of it." Miss Maudie explains to the children that
"People in their right minds never take pride in their talents..."
She explained that God-given talents are an uncontrollable human trait and, in Atticus' case, he was actually ashamed of his ability to kill with such precision. Jem understands his father's reaction, and warns Scout not to tell any of her classmates at school since
"If he was proud of it, he'd'a told us."
Jem recognizes that this is a gentlemanly attribute that he also wants to emulate.
"Atticus is a gentleman, just like me!"
The incident with the mad dog created a fundamental shift in the way Jem and Scout, particularly Jem, viewed their father. They found out that Atticus had at one time been an excellent shooter, the best in the county; they were incredulous, because Atticus, being the oldest father among kids their age, might as well have been one hundred years old, and since he wouldn't play rough sports like football, they viewed him as pretty worthless. As far as Jem and Scout were concerned, the sum total of Atticus's skills as a human being were practicing law and reading. However, when he managed to kill the rabid dog in one very accurate shot, and Miss Maudie set them straight on his shooting reputation as a young man, they were no longer ashamed of their father's perceived inadequacy.