Atticus knew his children well enough that if he had mentioned his ability with firearms, they would rely upon unfair power to resolve their problems. The root of social exploitation is the unfair use of power. The only resolve against the use of unfair power is to experience life in a sympathetic and empathetic way. He instead must have his children view life through the perspective of others. He knew that this knowledge would have his children idolize him for the ability to display of strength, where Atticus wanted to exhibit a strength of character instead.