Betrayal? Yes, exactly. If you think that cheating was not accidental, and he betrayed you, not only because it responded to the call of nature, but also because it really is: a false and fickle, it is better to release it to the world. Otherwise, to fight for such a man (and with such a man) you have a very long time. And the success of this struggle is questionable. To verify their assumptions about the nature of his windy, talk to him about it before parting frankly, but without yelling and battlefield dishes. And remember: if you are dear to him, and that was really a passing fancy, he will come back to you.
There are also a spineless guys hiding behind the mask of a steep macho their low self-esteem. Perhaps the girl with whom he will change, and he did not like, and he joined her in the relationship only for self-affirmation. But if you ask him about it directly, he can turn around and leave. For a guy should be the most extraordinary and loving. That he realized that he was lucky. But if he did not appreciate it, better to say goodbye.
If your guy is good in all respects, and in addition to this unfortunate mistake it practically nothing to reproach, think, and do not become your relationship too fresh? Or maybe you are too hard to push him to the registrar's office, and he is not ready yet, and it's a form of protest? Be honest with yourself and realize that you need a change to more of this happening again.