In this passage, President Kennedy uses irony to highlight the absurdity of the ongoing Cold War arms race and the excessive spending on weapons. He notes that "the expenditure of billions of dollars every year of weapons acquired for the purpose of making sure we never need to use them is essential to keeping the peace" (7), but then questions whether this is the most efficient means of achieving peace. By calling attention to the fact that these weapons are only meant to be used as a deterrent and will never actually be used, he is implying that the money spent on them could be better used for other purposes.
Kennedy also uses irony by pointing out that the pursuit of peace is not as exciting or attention-grabbing as the pursuit of war. He says, "the pursuit of peace is not as dramatic as the pursuit of war-and frequently the words of the pursuer fall on deaf ears" (7). This statement highlights the irony that even though peace is the ultimate goal, it is often ignored in favor of more sensational and destructive pursuits.
He also highlights the fact that the peace is rational thing to pursue, but it's more important than we think and the importance of peace is of an urgent task.
Overall, the passage uses irony to criticize the current state of international relations and call for a reevaluation of priorities.