@googlecoffee You are not responsible for your husband's cheating. He made a choice. He had other choices. He could have drug you to marriage counseling. He could have just left. He could have bought a relationship book and said, "let's work through this together." He could have just stayed miserable, or drank, or something else. He made a choice to cheat and he is responsible for that choice.
However, it sounds like your marriage already had problems. I say that not because he cheated or because he said that you shut problems down, but because you ask, " is everyone capable of being a cheat in a bad relationship?" To me, that seems like you owning there were already problems.
Does he want forgiven, or does he just want out?
Marriage is very difficult. People stay together through hard times because of children, or finances, or because they deeply hope it will get better. I think that its actually harder to tell the difference between a rough patch and the relationship being dead than most people realize.
karma said Somebody once told me that women in unhappy marriages leave when they can't take it anymore, while men in the same situation leave when they find someone else. this has been born out in our circle of friends, but talking to women where the man was the one who cheated and left, they already knew that the relationship has serious problems, they were just more willing to stay and hope it got better than the man was.
I also think that the state of a relationship is seldom one person's fault. The dynamic in a relationship is created by the two people. (The exception is when one person has a personality disorder / is abusive / etc.). In normal relationships, it's an interplay.