Is monogamy natural?

For a few years now, I've heard more and more people say something to the effect that monogamy is not natural. They base this on the fact that people want multiple sex partners even when they are in a relationship. That's why people cheat. So to embrace this more "natural" view, they either reject monogamy, opting for open relationships or pluralistic relationships, or they reject traditional marriage.

This strikes me as a mistaken line of reasoning. First of all, it's an argument that proves too much. If it's sound, then not only would it do away with monogamy, but it would do away with morality altogether. Morality is what adjudicates between which of your desires it's okay to give in to and which you should resist. If it's okay to give into any desire as long as it's natural to have that desire, then morality would have no place in the world. This would erase one of the most important distinctions between humans and the rest of the animal kingdom because then we'd feel free to endulge in our every desire. We would act purely on instinct, giving in to any natural urge that presented itself. It's perfectly natural to want to get revenge, to want to hurt people who wrong us in traffic, to want to tell lies to avoid uncomfortable situations, etc. But that doesn't make these things okay. So even if it's natural to want to have sex with multiple people even when you're in a relationship, that doesn't make it okay either.

Second, this line of reasoning leads to a contradiction. If we adopt the idea that our natural desires and inclinations are an indication of how we should live our lives, then that would both eliminate and justify monogamy. After all, it's just as natural to feel jealous and to not want your spouse to be with other people as it is to desire sexual relationships with other people yourself. If jealousy and a desire for your spouse to be sexually loyal to you alone is a perfectly natural feeling, then wouldn't that suggest, by the same reasoning, that monogamy is natural?

A lot of people try to embrace this open relationship idea or having multiple partners on the basis that monogamy is outdated, and they're getting with the times, but they still end up feeling jealous or having problems with it. They dismiss these problems on the basis that jealousy is immature and they just need to overcome it. But is it any less natural? Why isn't the inclination to embrace every desire indiscriminately considered immature instead? Isn't it children who whine and cry whenever they don't get everything they want? Isn't the mature thing to exercise self-control when it comes to inappropriate desires or desires that hurt people and damage relationships?

I think this idea that monogamy isn't our natural state just because people have desires and inclinations to stray from their partner is a really silly and immature excuse to live like animals.

EDIT: Wow. Just one day after posting this, I was on a discussion forum, and somebody said these exact words to me: "Were [sic] designed to be polygamous by nature and being in a 1 on 1 life partnership contradicts this."