In "Just Lather, That's All," the central conflict involves the barber's dilemma over whether or not he should kill Captain Torres. From a logical perspective, the barber believes that Captain Torres deserves to die because of the extreme violence he has demonstrated against members of the barber's rebel group. However, in the barber's opinion, murder is wrong, no matter what the circumstances, because it only serves to prolong the violence:
What do you gain by it? Nothing. Others come along and still others, and the first ones kill the second ones and they the next ones and it goes on like this until everything is a sea of blood.
Moreover, the barber prides himself on being excellent at his job and well-respected in his community. If he killed Captain Torres then his reputation would be in tatters because he used his razor, the symbol of his profession, against a defenseless client.
In the end, the barber resolves the conflict by deciding not to kill the Captain. In a final ironic twist, however, the Captain reveals that he came for a shave for precisely that reason. He heard a rumor that the barber wanted to kill him so he came to see if he would go through with it. Moreover, he shatters the barber's perception with his final words: "killing isn't easy."