Atticus makes this deal with Scout in order for them to keep reading together. If Scout tells Miss Caroline, who is a not only a new teacher but also new to Maycomb (she is from northern Alabama), she would continue to punish Scout. Atticus obviously does not want this. It likely reveals that Atticus recognizes Miss Caroline's need to appear like she is in control of Scout's education. Remember, she is making a big deal about bringing 'new' education ideas to Maycomb's school, notice Jem's reference to the Dewey Decimal System. Miss Caroline is unfamiliar with the families of Maycomb and their ways. Had she known Atticus at all, she would have realized that no one in Maycomb holds education in a greater light than he does. However, he realizes that Scout is special - as is their time together spent reading the paper each evening, which is why he has her keep quiet about their deal. This reveals too how crafty Atticus is. He is willing to keep things quiet to please everyone.