Saying something is natural tends to imply that we have no control over our "natures" so to speak and are predisposed to think and act in a particular way without the benefit of choice. It also suggests you have no choice but to give in to your natural instincts even if you don't like what your "nature" is driving you to do. It implies you have no free will.
Too often this kind of "natural" argument is used to justify cheating. If you love someone, it doesn't mean you may not find someone else attractive. Being monogamous means the person you're with is important enough to you not to compromise your relationship with. In this case, monogamy is a choice, even if it's not your 'natural" predisposition. You're choosing to focus your committment to one person rather than others or many. The whole "I just can't control myself or I just have to be with many people" argument is overdone.
Thing is, some people just don't want or can't handle the responsibility and accountability which comes with being committed to one person, so they use the "monogamy is not natural" argument to justify their infidelity or promiscuity. If you truly love and care about someone, you would want to give them all of you, not one part to them, and other parts to someone else or another set of people. Committed relationships go beyond simply fulfilling the desire to have your needs met. It values both the person and relationship and puts that first above everything else. Of course, it's understandable that if someone betrays the trust, then it may be difficult to remain committed.