How well can Atticus shoot and why did jem and scout have differences about it?

Since both Jem and Scout know of Atticus' great skill, Scout would want to brag to her fellow peers that her dad can do something good, and not have to be the only classmate without and exciting father. Jem feels completely the opposite way towards this, and he doesn't want to share this with his classmates. The reason why he doesn't want to share it because he realizes that their whole life, Atticus never mentioned ever shooting a gun. Since Atticus didn't mention this, then there is no reason to let out an unwanted secret of Atticus.