This relates to the themes of justice, kindness and mercy which are prominent throughout the book. Scout is about to kill the bug just because, being a young child, she is rather thoughtless, and simply because she has the power to do so. Jem, being older, is able to see that this is a thoughtless act of cruelty and there is no need for it, that people must learn to be kind and considerate towards all living things, particularly those that are smaller and weaker. The book shows however, that a lot of human beings don't subscribe to this notion; the lack of mercy shown to Tom Robinson is the most powerful illustration of this.
Jem's defense of the harmless roly poly illustrates the theme of pacification that Atticus exhibits throughout the novel. Atticus always turns the other cheek, preferring to fight his battles through reason and always without physical aggression. He gives up the rifle because his one good eye still leaves him with "an unfair advantage over most living things." He refuses to fight Bob Ewell after having been spat upon. He directs Scout to stop fighting with her fists and, instead, learn to control her temper without violence. Atticus and his children hold off the lynch mob without a punch being thrown. Jem has learned his lessons from both Atticus and the trial of Tom Robinson, where one of the novel's human mockingbirds is dealt both injustice and a bloody death. Jem is devastated by the biased jury verdict and its cruel aftermath: Tom cannot be helped, but Jem can stop Scout from needlessly taking the life of another innocent creature.