Why kill the dog?
When Atticus is handed the gun, he chooses not to kill the dog, but then he persuaded to kill the supposedly rabid dog. The dog was actually limping. Being a lawyer, he should have checked - limping does not mean dog-being-rabid.
If the point is of being protective about children, this point was blown out of propotation, when he clearly states to Jem that he would not be able to protect him or Scout all the time in a different scene.
So, why kill the dog?