Forgiving is something one does for oneself, not something one does for the other party.  

My husband puts it succinctly:  "Why would you allow anger for another to live rent free in your head indefinitely?"

But forgiving someone doesn't mean being willing to be a doormat for that person's bad behavior.  While I believe that, with few exceptions, most marriages can be saved if both parties wish to save them, the truth is that one party is always capable of undermining the marriage.  A serial cheater, a drug abuser, an alcoholic, a spousal or child abuser, can sink the ship of the marriage singlehandedly without help from the other partner.  (Spousal and child abuse situations are the rare cases in which I refuse to counsel women and men to remain with the abusive partner.  I would feel the same way about elder abuse.) 

In the case of drug and alcohol abuse, the addict him or herself has to make the change, and if they don't, the other partner must end the marriage for the good of all concerned, especially the addict.  However, I have known marriages to become much stronger after a struggle with one of these issues.

Cheating is more complex, and has more than one component.  I do not and never will 'blame' the innocent spouse for the actions of a cheating spouse, but it is true that typically (not in the case of serial cheating, but typically) there is some kind of mitigating factor at play that both partners have to look at in the cold light of day if they want to keep the marriage together.  Has there been a long separation for work or because of a family illness? Has pregnancy and childbearing and infant parenthood changed the dynamic between the partners? Is one of the partners suffering from depression? Is there a lot of financial stress (or other stress) in the household? Is the couple growing apart organically due to changing interests? 

So while you may 'forgive', that is not the same as living with the behavior.  Learning to trust again after a partner has cheated is a long, long process, and is fraught with setbacks.  No one can simply put the infidelity to one side and pretend it didn't happen, and this often feels to the partner who cheated like gestapo tactics ... the spouse checks her mate's email and cell phone records, looks in his pockets for receipts that don't belong there, calls him at work several times a day to check up on him, and so on.  This is all part of the trust reestablishment, and I tell spouses who cheated that this is part of the reengagement process.  It doesn't last forever, but it is uncomfortable for both partners while it does last.  The innocent spouse needs to feel secure; the cheating spouse needs to have his feet to the fire and feel uncomfortable enough that he won't want to experience that again (not that he would have the chance to experience it twice; she might forgive once, but not a second time).