Before we can create an outline for a comparison/contrast essay about these two stories, we have to have a firm grasp of the stories' themes, plots, and characters.
“Popular Mechanics” by Raymond Carver centers around a conflict between a husband and wife. The husband is leaving (and the wife decidedly wants him to), but he wants to take their baby with him. The wife disagrees vigorously, and a physical altercation ensues. The baby's father and mother pull him in one direction and then another until the child is screaming. The parents even fail to see the baby as a human being any longer. He is an “it,” an object to be won. Their whole focus is on winning the argument. The child no longer means anything. The story ends on an ambiguous note. Both parents are pulling on the child, and the narrator remarks, “In this manner, the issue was decided.” We don't know if the baby was badly injured or even killed, or if his father merely pulled him out of his mother's grasp. In any case, the situation is horrible.
“The Paring Knife” also centers around a conflict between a man and a woman, but it has a very different tone and very different results. This story is related in the first person; the narrator is the man. The narrator finds a paring knife under the refrigerator, and his mind goes back to the incident four years before that put it there. The man and his beloved had argued, and she kicked him out of bed. He was angry when he went down to the kitchen, and he knocked all the dishes onto the floor. Then he was horrified by what he had done and started to cry. His beloved came downstairs, turned on the light, looked at the mess (thankfully, not much was broken), and started to laugh. The tension between the couple broke, and they cleaned up the mess. The narrator now asks his beloved if she remembers the incident; she says nothing but slides the knife back under the refrigerator. It has become a symbol of a conflict solved, an argument that turned to laughter, and a strong relationship.
Now let's think about a possible outline for an essay about these two stories. One option would be to discuss one story at a time as above, analyzing how the characters and plot reflect on the nature of disagreement (the theme). The discussion of the second story would then comment on how it contains similar and dissimilar elements from the first story.
Another option would be to begin the essay by discussing the story's shared theme: disagreement between a man and a woman. Then, in a paragraph or two, discuss the stories' plots along with their similarities and differences and how they illustrate the theme. The next paragraph or two would focuses on the characters from the two stories, again delving into their similarities and differences and how they express the stories' various takes on the theme.