Quote 16
IAGO
I hate the Moor:
And it is thought abroad, that 'twixt my sheets
'Has done my office. I know not if't be true,
But I, for mere suspicion in that kind,
Will do as if for surety. (1.3.429-433)
We discuss this passage in "Jealousy," but it's important to the theme of marriage as well. Here, Iago suggests that his wife, Emilia, has cheated on him with Othello. Now, we know this is completely untrue. What we don't know is whether or not Iago actually believes that Othello has slept with Emilia. As we know, Iago lists multiple (and incompatible) motives for seeking to destroy Othello (elsewhere, he says he hates Othello because he was passed up for a promotion), so it's entirely possible that Iago's the one who makes up the rumor about Othello and Emilia. On the other hand, most men in the play assume that all women are promiscuous and unfaithful in general, so it's not so surprising that Iago would believe Emilia has been untrue.
Quote 17
IAGO
Now, I do love her too,
Not out of absolute lust (though peradventure
I stand accountant for as great a sin)
But partly led to diet my revenge,
For that I do suspect the lusty Moor
Hath leaped into my seat—the thought whereof
Doth, like a poisonous mineral, gnaw my inwards,
And nothing can or shall content my soul
Till I am even'd with him, wife for wife,
Or failing so, yet that I put the Moor
At least into a jealousy so strong
That judgment cannot cure. Which thing to do,
If this poor trash of Venice, whom I trace
For his quick hunting, stand the putting on,
I'll have our Michael Cassio on the hip,
Abuse him to the Moor in the rank garb
For I fear Cassio with my nightcap too, (2.1.313-329)
Iago is completely obsessed with infidelity. Earlier, we heard him say that he suspects Othello has slept with Emilia (a sentiment he repeats in this passage). Not only that, he also says he "fear[s]" that even Cassio is sleeping with his wife. What's Iago going to do about it? Why, he's going to try to sleep with Desdemona, which will allow him to get even with the "lusty Moor." If he can't do that, he wants to make Othello believe that Desdemona is screwing around with Cassio.
IAGO
She did deceive her father, marrying you,
[…]
OTHELLO
And so she did. (3.3.238, 241)
When Iago wants to make Othello suspect Desdemona's been unfaithful, he suggests a woman who disobeys and "deceive[s] her father is likely to screw around on her husband. Othello's response implies that he feels the same way. Instead of seeing Desdemona's decision to elope with Othello (despite her father's disapproval) as a sign of his wife's loyalty to him, Othello sees Desdemona's willingness to elope as a prelude to her infidelity. It seems that Othello's sexist assumptions leave him pretty vulnerable to Iago's plotting.