All I can say is if the person is not willing to consider anything past their own definitions of what they are comfortable with, no amount of explaining will ever convince them that Polyamory is a viable relationship choice. It'll always be an "excuse" to "break the rules".
My therapist asked me an interesting question: Who decides what is moral and correct for you? Should that decision be left for others to make?
My point is, you can't convince people of anything they aren't ready or willing to accept as a possibility. All you can really do is live life as vibrantly as you can and live by your own moral compass.

Cheating hurts, period. It robs your partner (or society at large) of something of value be it an experience or an intangible like time and energy. It can also rob your parnter or society of something tangible like items or money. By that logic anything you do that doesn't rob a person of something they value ISN'T cheating.
My partners do not value monogamy but they do value honesty. Being with someone other than my husband doesn't cheat him of anything he values but lying to him does. Likewise with my life partner. Therefore, polyamory isn't sanctioned cheating because nothing I do polyamorously, and honestly, robs my husband of something he values. It's not cheating at all!
Here's another way of looking at it....If I smoke and it's well established that I smoke then smoking is not cheating. If, however, I announce that I am going to quit smoking for whatever reason and then I sneak off to be alone to smoke then I have CHEATED on my promise to quit smoking. That part is well understood.
BUT if it is understood that I want the right to have a smoke in private while I am quitting and I sneak off to do this then it really isn't cheating because I am not breaking my word. Likewise if I announce that I am going to have a smoke...by definition it is not cheating because I am not breaking my word.
The problem is many people will argue that because smoking is dangerous to the health of the smoker and those around them that ANY cigarrette (cigar or pipe whatever) smoked by a person trying to quit is cheating no matter how hard they try to be up front and honest.
It's the same with people who fear polyamory...and yes it IS fear that drives them to try to poke holes in every 'argument' they don't agree with. I have not, in all my time as both an openly pagan and polyamorous person met someone who viciously opposed my choices who wasn't afraid of something about them. In my experience truly fearless people may not want to live as I do, but they don't really care to debate the finer points or accuse me of having negative desires or goals.

Pick your battles and speak only when your words might be met with an open mind. This will save you alot of heartache and headaches. less