The situational irony at the heart of “An Encounter” is that the narrator craves—and creates the prime conditions for—adventure, only to end up running away from it. The following passage, from early in the story, establishes his deep desire for adventure:
[W]hen the restraining influence of the school was at a distance I began to hunger again for wild sensations, for the escape which those chronicles of disorder alone seemed to offer me. The mimic warfare of the evening became at last as wearisome to me as the routine of school in the morning because I wanted real adventures to happen to myself.
Here the narrator explicitly states that he desires “real adventures” which he associates with “wild sensations” and “chronicles of disorder.” This, he believes, will be the antidote to “the routine of school” and the “weariness” he feels in his day-to-day life.
The irony, of course, is that the narrator does end up experiencing “wild sensations” and “disorder” when he meets the pedophilic old man, meaning the interaction technically fulfills his criteria for adventure. Despite the "opportunity" for adventure that the man’s strange and increasingly threatening behavior grants the narrator, he ultimately runs away from the man, feeling his “heart […] beating quickly with fear.”
While the narrator clearly made the right choice for his safety, he ends up feeling “ashamed” that he could not be a hero. This moment of irony highlights how the types of adventures the boy craves are not available to him as a child in Dublin—the only choice he has is between the mundanity of everyday life or the less-than-romantic threats present within the morally decaying Irish society.
