Well, it sure isn't nature that caused monogamy. So since nurture is responsible for monogamy, I would assume nurture (or the lack there of) is also responsibly for cheating.
Biology teaches that men generally want to spread their seed as wide as possible, and women want to secure help with child rearing (monogamy). So that is where we start. But women can secure a man's help today (financially at least) without being faithful to him (she'll get the kids and child support regardless of who causes the divorce). And, men have often been nurtured into monogamy as a condition of being allowed to spread their seed (and nurtured to believe that helping shape children from one women is better than having a lot of children with different women that they don't' get to help shape). So, nature and nurture get muddled together on this.
But I stand by my original statement, that monogamy and/or cheating are primarily today caused by nurture. If we followed nature, men would just rape women when they were horny.