Understand that there are people without whom you are unhappy, but they are happy without you
Every person in this world has a right to live life as he chooses. He has a right to be with whoever he desires, and not to be with whoever he does not desire. If you accept and honour this fundamental right, you should paradoxically be the first to support an unfaithful partner. By his action, he has made it clear that he is able to betray your trust at any time, so enable him to leave, even more so, if you sincerely love him. After all, his happiness is unconditionally important to you in such a case. Does it sound hard? In the following lines, I will explain why letting go is the best service you can provide both to an unfaithful partner and (especially) to yourself.
The problem for too many people is that they love conditionally. By their approach they say: “I love you, BUT ONLY as long as you are with me. Otherwise, I wish the worst for you.” If you love someone, then your primary concern should be that your partner is happy, regardless of the circumstances. That is, whether he is with or without you. If a partner lets you know that he is happier with someone else, simply because you love him, you should support him on his way to happiness, and prove that he can rely on you. Even if this means he is leaving you. Otherwise, you are only pretending that you care, while in fact behaving possessively and selfishly. I do not believe that anyone wants to live with a possessive egoist. Or with somebody who does not wish to stay in the relationship. Therefore, do not hurt yourself. Let him go, if he wants to. This is necessary in your own interest.