Atticus does not, as one might carelessly assume, give Scout and Jem guns so that they can learn to shoot. He has more complex reasons than that:
First of all, he gives the guns to his children to teach them responsibility. Guns, even airguns, are weapons, and giving them to Scout and Jem requires that they take a certain degree of responsibility for their actions and decisions. He explains to them, "I'd rather you shot at tin cans in the backyard, but I know you'll go after birds. Shoot all the bluejays if you want, if you can hit 'em, but remember it's a sin to kill a mockingbird" (92). Rather than threatening or bribing his children to do something he wants them to do, he explains what he would like and what he believes is wrong to do. Then, he lets them make their own choices.
Atticus also uses guns to teach his children modesty and perspective. Atticus is pretty wholly against gun violence, he also reveals that he was one of the deadliest shots in town when he kills a rabid dog. The children are stunned by his prowess and confused by it until a neighbor explains, "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 until he had to" (101). Rather than bragging or using his talents indiscriminately, Atticus thinks critically and uses his skills when he has to, understanding their impact.