Obviously, in some sense, if I don't actually act on that desire, then I don't *really* want to, but in another sense, I still really do--and the only thing that's stopping me is my fidelity to my partner.
From my partner's perspective, I don't really see the difference between having a certain serious desire and my actions being consistent with that desire. If my partner is concerned with monogamy, then my non-monogamous desire seems to be a breach of the intent of that partnership.
It seems that monogamy--if appropriate at all (which is another discussion entirely)--should be something that happens naturally in a relationship rather than imposed as some kind of add-on. It strikes me as odd that either partner should feel compelled by the label to be monogamous.
One answer might be to reevaluate whether I should be in a relationship with this other person if I still want to have sex with others, but I find this suggestion unsatisfactory because the relationship may nevertheless be a great value--and then perhaps I'm stuck suffering a persistent, insatiable lust for others.