The tone of “The Curious Case of Benjamin Button” starts out ironic and judgmental before moving into a more earnest and tender place. The following passage from the beginning of the story—in which the narrator gives an overview of the Button family—captures the initially ironic tone:
The Roger Buttons held an enviable position, both social and financial, in ante-bellum Baltimore. They were related to the This Family and the That Family, which, as every Southerner knew, entitled them to membership in that enormous peerage which largely populated the Confederacy. This was their first experience with the charming old custom of having babies—Mr. Button was naturally nervous. He hoped it would be a boy so that he could be sent to Yale College in Connecticut, at which institution Mr. Button himself had been known for four years by the somewhat obvious nickname of “Cuff.”
Specific phrases here show that the narrator is gently mocking these characters. Take, for example, the assertion that the Buttons “were related to the This Family and the That Family.” By not actually naming the families, the narrator implies that, unlike the Buttons, they do not care about the specifics of the upper-class Baltimore social scene. The narrator’s distaste with this particular elite social strata also comes across when they describe how Roger had “the somewhat obvious nickname of ‘Cuff.’” Because wealthy people associate buttons with cuffs of shirts, Roger "Button" receives this “somewhat obvious” nickname.
The narrator’s mocking tone eventually shifts into a more earnest register as Benjamin’s experience is less centered on the spectacle of being a young man in an old man’s body and more centered on the sadness inherent in being an old man slowly moving toward infancy and death.