The dramatic irony in Cecily and Gwendolen arguing about who has claim to Ernest lies in the fact that neither of them actually knows the truth about Ernest. Both women believe they are engaged to a man named Ernest, but in reality, Ernest doesn't exist—the two men they think they are in love with are actually Jack and Algernon, who have been deceiving them by pretending to be someone they are not. This creates a humorous and ironic situation where the women are arguing over a man who doesn't even exist, highlighting the theme of deception and mistaken identities in the play.
