Prior to the incident with Tim Johnson's dog, Scout relates that both she and Jem feel that Atticus acts older than most other children's fathers. Atticus is not athletic. The children both feel that they have nothing to brag about their father. At the beginning of Chapter 10, Scout adds that whenever Jem would ask to play tackle football, Atticus would say "I'm too old for that, son." Atticus doesn't do anything the children would think is "cool" or interesting to other children their age:
Our father didn’t do anything. He worked in an office, not in a drugstore. Atticus did not drive a dump-truck for the county, he was not the sheriff, he did not farm, work in a garage, or do anything that could possibly arouse the admiration of anyone.
Scout even mentions the fact that Atticus wears glasses, as if that makes him seem even older. He doesn't hunt, fish, play poker, or drink. In short, they think he is boring. When Atticus shoots the rabid dog, they finally have something to brag about to the other children. Scout can't wait to do this. But Jem has a revelation. He understands that a gentleman doesn't brag about himself. Also, Jem understands that Atticus would never brag simply to impress other people. He lives by his actions and his words. Jem decides he wants to act and behave the same way. He looks up to his father in a different way at this moment.