The irony lies in the contrast between her outward appearance and lifestyle (modern, sophisticated, seemingly detached) and her inner life and relationship with the narrator. She presents a certain image of independence and worldly knowledge, yet her emotional connection to the narrator and her reliance on the country grandmother for a deeper understanding of family history reveal a hidden vulnerability and dependence that contradict her projected persona. This contrast between her presented self and her true self is the source of the irony.