Before this event, Jem and Scout looked at their father as loving and intelligent, but weak. After learning that he has this skill, they no longer think so. Scout wants to tell others about her father being the best shot in Maycomb, but Jem won’t let her because, in his maturity, he understands why Atticus has hidden this talent from the children. Atticus is not the kind of person who would be proud of an ability which is even potentially violent (shooting).
Atticus is not one to flaunt his abilities. It is in his nature and his philosophy that violence is always a last resort. So, as part of his living example to his children, he would only use a gun in extreme situations, such as this one with the rabid dog. Atticus could easily show off his talents (shooting, checkers and so on) but another lesson he teaches the children, central to the trial, is that one should not do things just to please the majority or simply to brag that he is better than other people. One should not conform just to gain acceptance. He does what he has to – when he has to do it. Bragging (or even showing modest pride) about a talent, especially one which inflicts violence, is completely antithetical to Atticus’ own philosophy and the lessons he wants to teach to his children.
Atticus Finch is not only the father of the young protagonist of Harper Lee's novel To Kill a Mockingbird; he is also the novel's moral conscious. An infinitely decent and wise lawyer dedicated to the pursuit of justice, he is raising his children with the same values that shaped his character. In addition, Atticus, Scout emphasizes in Chapter 10, is relatively old to be the father of young children. He appears to Jem and Scout as "feeble" and unable to parent the way younger couples are seen parenting. As if to further emphasize the point, Scout goes on to say:
"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 is six years old and Jem is ten when To Kill a Mockingbird begins. They are too young to understand much that occurs in the world, existing as they do in the small town of Maycomb. To children of such age, a profession like lawyer is hardly the stuff of which dreams are made. Finally, Atticus eschews the use of firearms. Scout notes in this chapter that when Atticus presented his children with air-rifles, he refused to have anything to do with the guns, including teaching his children how to use them. Scout quotes Uncle Jack as asserting that "Atticus wasn't interested in guns."
Atticus's aversion to guns assumes considerably greater significance later in Chapter 10 when Maycomb County Sheriff Heck Tate enlists the lawyer's assistance in shooting a rabid dog. When Atticus, with much prompting by the sheriff, takes the rifle, aims and fires, killing the dog with one shot, Scout and Jem are astonished to discover their feeble, old father is actually an expert shot. The answer to the question--why did not Atticus ever tell his children about his prowess with a rifle--lies, perhaps, in Miss Maudie's discussion with Scout and Jem:
"If your father's anything, he's civilized in his heart. Marksmanship's a gift of God, a talent.... 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."
Atticus never discussed his skills as a marksman because he was an inherently modest and decent human being who didn't like killing anything. When he presented the air-rifles to Jem and Scout, it was with the proviso that they never shoot at any living thing. A realist, however, he recognizes that, being children, they will be tempted to shoot at birds, providing the novel's central theme: "shoot all the bluejays you want...but remember it's a sin to kill a mockingbird." Atticus never told his children about this particular skill because, besides being modest, he takes no real pride in it.