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As for Iago’s jealousy, one cannot believe that a seriously jealous man could behave towards his wife as Iago behaves towards Emilia, for the wife of a jealous husband is the first person to suffer. Not only is the relation of Iago and Emilia, as we see it on stage, without emotional tension, but also Emilia openly refers to a rumor of her infidelity as something already disposed of.
Some such squire it was
That turned your wit, the seamy side without
And made you to suspect me with the Moor.
At one point Iago states that, in order to revenge himself on Othello, he will not rest till he is even with him, wife for wife, but, in the play, no attempt at Desdemona’s seduction is made. Iago does not encourage Cassio to make one, and he even prevents Roderigo from getting anywhere near her.
Finally, one who seriously desires personal revenge desires to reveal himself. The revenger’s greatest satisfaction is to be able to tell his victim to his face – "You thought you were all-powerful and untouchable and could injure me with impunity. Now you see that you were wrong. Perhaps you have forgotten what you did; let me have the pleasure of reminding you."
When at the end of the play, Othello asks Iago in bewilderment why he has thus ensnared his soul and body, if his real motive were revenge for having been cuckolded or unjustly denied promotion, he could have said so, instead of refusing to explain.
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W.H. Auden (The Dyer's Hand and Other Essays)