Thornton notes that "the rage of Caliban at not seeing his face in a mirror" alludes to the preface to The Picture of Dorian Gray (1891), by the great fin de siècle Irish writer and wit Oscar Wilde (1854-1900). Wilde defines the two great movements in nineteenth century British (and French) literature in terms of the reactions of the reading populace: “The nineteenth century dislike of Realism is the rage of Caliban seeing his own face in a glass. / The nineteenth century dislike of Romanticism is the rage of Caliban not seeing his own face in a glass.”
Wilde’s meaning seems clear enough: the benighted bourgeois are like Caliban, the anti-hero of Shakespeare’s The Tempest—bestially resistant to all civilizing influences. When realistic art accurately imitates them, they are outraged to see themselves represented so unflatteringly. But when romantic art offers an alternative, expressing the avant-garde genius of the artist rather than representing the mediocrity of his audience, they howl in protest at not seeing anything like themselves.
It is much less clear why Mulligan should compare Stephen to the critics of romantic art, since Stephen himself is a romantic artist. Probably Mulligan does not intend any exact analogy, but is merely playing with the implicit contrast between external reality and subjective experience: i.e., Stephen is appalled by his appearance in the mirror because it corresponds so poorly to his internal self-conception. If this is the case, then he is stating in his own way what Stephen has already thought about himself, using Burns rather than Wilde as a touchstone: “As he and others see me. Who chose this face for me?”