The demons begged Jesus, “Send us among the pigs; allow us to go into them [pigs].”

-Mark 5:12, NIV

Cheaters often do not want to face the truth.

Confronted with the truth about how evil their behavior is, some choose to run away or blame the faithful spouse. The truth burns.

A cheater who has no good, biblical reason to divorce is a classic example of this situation. They are confronted by Scripture and become enraged by the truth of their situation.

The problem is how the Scripture makes it clear their choice to divorce a faithful spouse is a sinful one. They want absolution for their treachery, and the Bible does not give that to them. It is not what they want to hear.

Personally, I wonder about the demonic aspect of infidelity in these matters.

Truth and the Bible are not favored by the demonic. They certainly are not liked when applied as a restraint to wicked behavior. 

I suspect some degree of the demonic is involved simply by how common the lies are that cheaters speak as well as how common their response is to inconvenient truth about their sinful behavior.