Why did Atticus want Scout to overhear his conversation with Uncle Jack in To Kill a Mockingbird?
I believe that Atticus allows Scout to purposely overhear his conversation with Jack for two reasons. First, Atticus has not found a way to sit down and explain to his children about the upcoming trial and the implications it will have on the family and community. By frankly discussing the Tom Robinson trial with Jack, Scout is able to hear Atticus's side of the story and his own reasons for taking the case: It is in part because Judge Taylor appointed him to do so, but he also took it because of his children.
"... do you think I could face my children otherwise?" (Chapter 9)
(Oddly, Scout must not have understood her father when he explained to Jack that Judge Taylor told him " 'You're It.' " Scout only learns this later when she hears members of the Idlers' Club discussing it.) The second reason Atticus allows Scout to hear his conversation is to show her how proud--and forgiving--he is of her recent behavior. Scout has been forced to listen to her classmates ridicule Atticus for being a "nigger-lover," and to her cousin Francis claim that her father is "ruinin' the family." Scout defends her father by fighting Francis, but is in turn spanked by her Uncle Jack for doing so.
"... I hope and pray I can get Jem and Scout throuugh it without bitterness... I just hope that Jem and Scout come to me for their answers instead of listening to the town. I hope they trust me enough..." (Chapter 9)
Atticus is trying his best to prepare Scout for the upcoming trial and all its accompanying tribulations. He knows that Tom has no chance of acquittal; he knows that children at school will say all kinds of mean things to Scout; and he knows that life for the Finch family in Maycomb is going to get much more difficult. Atticus could've just sat Scout down and told her all this to her face, but he's chosen not to.
However, there's a method to Atticus's approach. If Scout has to find out all this vital information by eavesdropping then it means she has to listen very carefully to what's being said. That way, Atticus's words will have a more profound, lasting impact upon her than if her father had just came right out and told her directly. Most people, especially children, are intensely curious to find out what other people are saying about them. Atticus wants Scout to feel like she's privy to some special secret that she really shouldn't know about. Children like secrets; and they like it when they're being let in on one. Atticus understands this, hence his intention that Scout should hear his every word.