Atticus feels like he shouldn't shoot. He believes he has an unfair advantage over other living things because he is really very good at shooting. Readers do not discover this detail until chapter 10. He gives the rifles to the children in chapter 9:
"Don't point them in the house," said Atticus, when Jem aimed at a picture on the wall.
"You'll have to teach 'em to shoot," said Uncle Jack.
"That's your job," said Atticus. "I merely bowed to the inevitable."
Here in chapter 9, he gives the job to Jack to teach the children, but does not state why. In chapter 10, readers begin to learn why as Scout narrates:
When he gave us our air-rifles Atticus wouldn't teach us to shoot. Uncle Jack instructed us in the rudiments thereof; he said Atticus wasn't interested in guns. Atticus said to Jem one day, "I'd rather you shot at tin cans in the back yard, but I know you'll go after birds. Shoot all the bluejays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird."
This seems to be important since it is the book's title. He expresses that there are things in life that need to be destroyed (like blue jays), but most things in life are innocent (like mockingbirds). This language is strong because Atticus had never used the word sin with the kids before.
Finally, in the end of the chapter Miss Maudie indeed explains the reason WHY Atticus does not teach the children... he is too good:
"If your father's anything, he's civilized in his heart. Marksman ship's a gift of God, a talent --- oh, you have to practice to make it perfect, but shootin's different from playing the piano or the like. 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."
He didn't have to teach the children, that was something Jack could do. Atticus had vowed to only shoot when he needed to.