You can never be certain of fidelity, only infidelity, and this partly explains Iago’s success. The faithfulness of a spouse is not, simply not, something one can establish definitively; on some level, it must be taken on faith, which means on mystery, which means accepting or even embracing mystery as a part of one’s life—but is there any part of any person’s life more important than this? The stakes are almost incomparably high.
In a sense, then, the question Iago poses is simply a choice of pains. To persist in loving Desdemona is to persist in having faith in Desdemona, and to have faith in Desdemona is to believe that she’s been faithful—believe; again, not know; but rather, to trust her, and to absorb, along with that trust, Othello’s neverending fear that he could be wrong.
The other option, of course, is to pursue a final and conclusive ruling on the question of Desdemona’s fidelity. But once more, suppose the husband confirms that his wife has been faithful to him? At best he might confirm that on this day, with this particular man, Desdemona was not adulterous. But this manifestly cannot be done for every single case. Even the attempt to achieve such comprehensive exculpation would so crowd the husband’s attention that he could never do anything else. And there would always be an argument that something got missed, a clue got overlooked. A fact not checked, a question not asked.
Iago succeeds, in part, because the establishment of Desdemona’s adultery is a release from the bottomless anxiety Othello would otherwise have to live with. He chooses the pain of knowledge over the pain of doubt.