The concept of Catch-22 presents a paradox where characters find themselves trapped by contradictory rules. In the case of Orr, he faces a dilemma between flying dangerous missions and preserving his sanity. If he chooses to avoid the missions, his decision signifies that he is rational and must fly them; however, if he goes through with them, he is deemed insane and would be relieved from the requirement.

This circular reasoning exemplifies the absurdity of war and the bureaucratic systems that govern soldiers' lives. The nature of Catch-22 illustrates how individuals can be ensnared in situations where any choice leads to a negative outcome, emphasizing the futility and helplessness in facing such illogical constraints.