It's very important that anyone - man or woman - is honest with themselves about why they want to stay in their marriage after an affair is discovered and to ensure that their decisions are not disproportionately affected by the ties that bind and other personal issues such as pride and ego. Then they need to make a decision based on their partner's actions after discovery, not their words.
However, not everyone is a 'cheating swine' in the sense that this defines them as a person. There are many people for whom this was a once-in-a-lifetime terrible mistake that was deeply regretted and will never be repeated. These are the people who deserve to be forgiven, but only if they are willing to work on the factors that led them to make those mistakes.
It's also a great opportunity for their partners to re-define their own lives, get the relationships they really want and to focus on the things that make them happy as individuals and not just within the relationship.
Couples who approach it this way are not demeaning or kidding themselves. On the contrary, their decisions are often far clearer-sighted than before when there was blind trust and complacency that despite being fallible human beings, they weren't capable of making mistakes.
If people's only experiences of infidelity are of men who weren't willing to make those changes, or of men engaged in long-term deceits towards their partners and one's own collusion in that, then this will inevitably colour opinions and advice, but not all men and women are like that and not every infidelity follows those two patterns.
Often after infidelity, the focus is on the relationship and/or the person who has broken the trust, but it's as important to concentrate on the person who was faithful and his/her response to it. Some people 'lose themselves' whether they remain in the relationship or not, but others approach it differently and choose experiences that build and reinforce their esteem, rejecting those that come from a desire to hurt oneself and others.