Atticus is old and Scout and Jem want to be proud of him at school with some sort of special bragging rights.
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Atticus is a humble man. He is, in every sense of the word, a gentleman. When Atticus shoots the dog, it is out of necessity. Both Jem and Scout love and respect their father but find him on the boring side. When he shoots the dog, the children are speechless. Heck Tate makes the complement but Atticus does not want the fuss. Boasting, even by someone else, is not in Atticus's nature. Guns are certainly not something that Atticus wants to be associated with. Still everyone is duly impressed.