The golden rule for arguing about morals is the golden rule itself: One should treat others the way one would like others to treat oneself.
Picture yourself being cheated on. It is quite miserable knowing your partner has broken your trust. That the special exclusive bond you shared with him/her was never exclusive or special. It would feel like such a violation and make you doubt your own self-worth, that maybe you aren't deemed worthy enough. A relationship is heavy, involves a lot of opening up and intimacy, and breaking that trust makes you feel vulnerable and betrayed. The searing mental image of your loved one being intimate with someone else is hard to erase completely from your head, and would haunt you for long. Its a shattering blend of impotent anger, envy, loss of self-confidence, possible erosion of faith in love, disgust at having opened up to such a person, and mind-numbing regret and sorrow.
Why would you do this to anybody?
Again, the moral aspect comes in mainly because of the breach of trust.