When we think about the climax of a story, we can think of it in two different ways. First, we can think of it as the turning point where the main character makes a decision and/ or takes an action that sets up the resolution of the conflict, for good or for ill. Second, we can think of it as the high point of the story's action where the reader experiences the most tension, after which the tension subsides as the story's action falls.
In "Once Upon a Time," the climax according to the first approach occurs in the penultimate paragraph when the family installs the "razor-bladed coils" atop the walls around their house. This is the decision that finally resolves their fears so they can stop worrying about invaders. Until this point, the statement "You're right" often precedes the family's next effort to improve their security. Now, the statement "You're wrong" appears, signalling a change. This coil will never rust; even the cat doesn't try to get through anymore. Yet this success in achieving their security sets up the resolution of their conflict—they have kept outsiders away but lose their son as a result.
The second approach of identifying a climax leads readers to the final paragraph where the little boy gets caught up in the razor-bladed coils. When he "screamed and struggled deeper into its tangle," the high point of tension in the story is reached. Now the threat to life and limb that the family has feared comes about, albeit not in the way they feared. They have inadvertently caused the destruction of their most prized "possession," their son, through their efforts to keep away what they feared.
Thus, readers can think of either the family's installation of the coil atop the wall or the little boy's getting caught in the coil as the climax of the story.