One reason is that he wants to chastise her for her "hotheadedness" because Atticus is worried about what is coming up. He uses his conversation with Jack to voice some concerns; he hopes that Scout will pick up on them, and take them more to heart than if he had given her a direct lecture. Since Scout has already lost her temper twice over even the mention of Atticus and his trial, he is worried that "Scout'd just as soon jump on someone as look at him if her pride's at stake". He hopes that Scout can get through the trial "without bitterness...[and] that Jem and Scout come to me for their answers instead of listening to the town. I hope they trust me enough." He is telling Scout that she is going to have to be calm, steady, and come to him if there are difficult times, instead of fighting or endorsing other people's beliefs.
His conversation with Jack is a kind of preparation for Scout, to bolster her for what is around the bend. He is concerned, and that worry spills over in this conversation.
Miss Maudie indicates that Atticus is "civilized in his heart" and didn't want "an unfair advantage over most living things", and so he doesn't boast about his talent. He realized it was a gift, and to brag about it would just make others feel bad, so he doesn't.