Making Jem read to Mrs. Dubose as a means to make amends for destroying her flowers is the lesson he first and foremost wants to teach. No matter how angry someone makes you, you shouldn't retaliate with physical violence. I don't think he wants Jem to read to her out of a sense of sympathy -- that would change the dynamic of the situation. Jem has to feel is doing this to redeem himself -- later he can learn how this was as much about Mrs. Dubose and it was about Jem.
Once Mrs. Dubose dies, Atticus reveals the full story of her drug addiction and subsequent determination to kick the habit and die free of the drugs. With this information he can teach another couple of lessons. First he can give thes kids a definition of courage that isn't just physical displays like shooting guns. He can also use this situation as another example of not judging people until you can imagine having stood in their shoes.