Why is it ironic that Richard Cory takes his own life?

Edwin Arlington Robinson’s narrative poem “Richard Cory” ends with the suicide of the poem’s eponymous character. In the final lines of the poem—which is written in four ABAB quatrains—we learn that:

And Richard Cory, one calm summer night,
Went home and put a bullet through his head. (15-16)

The irony of the poem is produced through this sudden and unexpected reversal. The first three stanzas of the poem depict the town’s admiration of Richard Cory, who we learn is “richer than a king” and “admirably schooled in every grace.” While Richard Cory occupies this seemingly privileged position, the rest of the town “Went without the meat, and cursed the bread” (14). The suffering of the speaker is juxtaposed with the wealth of Richard Cory, further accentuating the surprise and irony of the poem’s conclusion: we expect Richard Cory, this kingly man, to be happy. But we learn that, at least in this situation, appearances are deceptive.
Despite the appearance of a happy life, Richard Cory’s end is a tragic one. This deception is formally presented in the poem through its rhyme scheme. The quatrains are iambic and thus melodic at times, but there is one moment in the second stanza that suggests all is not as it seems. Although the poem employs an ABAB rhyme scheme, this rhyme scheme is deceptive at times. Consider lines five and seven, which end with “arrayed” and “said.” These two words produce a visual rhyme—that is, an eye rhyme—that is not audibly consistent with the rest of the poem. Here, the form tells us the same story as the poem’s narrative, formally foreshadowing what is to come. Appearances can be deceptive, and that which seems happy can be truly tragic.