A cheater must want to stay with their partner, since they're not leaving. This suggests several possibilities to me: (a) co-dependency... they hate their partner, but are afraid to leave them anyway (b) a partially-fulfilled sense of duty, maybe sticking with the partner for the sake of their kids but trying to sneak what they really want on the side (c) they may like their partner but aren't getting the sex they crave (d) they're polyamorous but are afraid to be open about that (e) their partner has money/power they want to keep their hands on.
None of those causes justifies the cheating, but I do have sympathy for most of them. Rebuilding trust would be difficult, but to just categorically rule out forgiveness without considering the specific situation seems a bit narrow-minded. If the reasons were fully addressed and the lies hadn't dragged on too long or gotten too complex, the relationship might be able to continue. Even if it's time to part ways, one can forgive without forgetting and without making the mistake of trusting them again. Of course I wouldn't forgive myself if I betrayed trust like that, but we should hold ourselves to higher standards and try to give other people more of a break.
(Disclaimer: cheating has never been an issue that affected anyone in my life, so I lack the emotional familiarity and am just presenting an analytical view. My view, however, is that the analytical view should ideally trump the gut instinct even though it rarely will.)