Final answer:
The irony of the statement lies in the characterization of the situation as 'sickeningly comic' when it is not funny, and the men's whispers indicating the gravity of the circumstances.
Step-by-step explanation:
The quote "there followed what I later realized was a sickeningly comic aspect of an unfunny situation; the men talked in whispers," presents a situation filled with irony. The irony lies in the juxtaposition of something being 'comic' within a context that is distinctly not funny—highlighting a contrast between the expected reaction to a comedic situation and the reality of the gravity of their circumstances. This contrast is further sharpened by the fact that the men spoke in whispers, which generally conveys a need for secrecy or the seriousness of a situation, rather than the openness associated with comedy. The irony may arise from a defensive psychological mechanism, where the characters might cope with stress or danger by perceiving or behaving in ways that are incongruous with the severity of their environment.