Act I scene 1 contains a great example of treachery followed by loyalty on the part of Iago. He tells Brabantio that his daughter is with Othello, hoping to incite a rage against Othello who is not really approved to be with this nobleman of Venice's daughter. He then immediately returns to Othello trying to show his loyalty as he warns him of the coming anger at he and Desdemona's marriage.
Act II scene 3 contains the bit with Iago telling Roderigo to just be patient, that he will still get him what he wants, namely Desdemona. Yet Iago is keeping Roderigo around simply as a piece of his plan, again a very clear combination of loyalty and treachery at the same time.
Another example of loyalty and treachery right together is when Emilia is loyal to Iago in giving him the handkerchief which he asked for, and unknowingly she is helping to serve his treachery upon her lady's master, Othello.
Loyalty and treachery are prominent themes in Othello. Treacherous characters manipulate loyalty and good faith—this is the ultimate betrayal of trust. Iago is treacherous, and he is so good at it, that even when he admits it in the lines, "I follow him to serve my turn upon him" (I.i.42), and "In following him, I follow but myself" (line 59), it goes unrecognized by the gullible Roderigo. Iago is a master of deceit and is able to turn any circumstance to his own advantage.
A good example of loyalty versus treachery exists in Act II, Scene iii when Iago feigns friendship with Cassio and then ensures he gets drunk so that Cassio will disappoint Othello. This begins the chain of events so necessary to convince Othello of Desdemona's infidelity. Iago carefully sets himself up to receive Othello's praise for defusing the situation, and Iago earns Cassio's trust as he tells Cassio not to be so hard on himself. When Iago offers Cassio advice, suggesting that he asks Desdemona to plead his case, "entreat her to splinter" (314), Iago knows that Desdemona will be happy to help, and his treacherous plot becomes even more cunning.
Desdemona is the ultimate loyal wife, and, sadly, Othello is the betrayer. Othello, unlike Iago, does not set out to betray his wife, and genuinely believes that she has betrayed him. It is Iago's treachery (far worse than betrayal) that has convinced Othello to the point that he will not listen to Desdemona's reasonable responses, or "send for the man and ask him" (V.ii.53). In Act III, Scene iii, Othello insists that Iago provide him with "ocular proof" (364) of Desdemona's affair. Iago, still berating himself for bringing the news to Othello, talks about a dream Cassio is purported to have had, and ultimately tells him about the handkerchief which Cassio now has. Iago knows that Othello is no longer thinking rationally, and reminds Othello that "it speaks against her with the other proofs" (line 445). Othello is almost past the point of no return when he says, "Arise black vengeance" (451), and yet Iago continues and even pleads that Othello, after taking vengeance against Cassio, let Desdemona live. He knows his subject well enough to know that this will only urge Othello more.
In Act V, Scene ii, Emilia still refuses to believe that Iago could have been instrumental in the previous events, especially in Desdemona's death. Previously, Emilia's loyalty was tested when Iago asked her to take the handkerchief from Desdemona, and she refused. Loyal as ever, however, she does give it to Iago after finding it on the floor. She now pleads with Iago to tell her that he never told Othello that Desdemona was "false." Iago insists that Emilia should go home, but her loyalty to him is no longer a concern to her. Her loyalty to the memory of Desdemona, "so good a wife" (237), is more important, even to the point of her own death at Iago's hand.