Research has shown that the cheated partner has a harder time healing from the unfaithful partner’s deceit than the cheating itself. Some people leave the other person even if they cheated once because of the unfaithful partner’s deceit and refusal to come all clean and transparent about the cheating and not the cheating itself/habitual cheating.
This makes sense to me because unless you come clean about your cheating then there can be no grounds to guarantee it won't happen again. If you don't admit the mistake then maybe you don't see it as such and will definitely do it again.