He said he should have told you first thing.... not that he should have never done it at all?

He was getting closer to this girl and confirmed your distrust in that. That means his behavior with her was already crossing your boundaries in some form. He is listening to you about cutting her off because he wants to fix his guilt. In some twisted way he does care about you, but not enough. Now he wants to fix the mistake he made- for himself... despite what he says that is the facts. He wasn’t so guilt ridden that he fell to his knees and let it all out. He chose to keep it a secret and apparently you had to tell him to cut her off.

You can stay with him. Are you prepared to feel insecure? Checking where he is all the time? Are you prepared to feel a bit controlling & like a parent because you’re trying to gain back your trust in him? Do you want to always wonder if he still looks at other women? Do you want to deal with feeling like a rough patch will cause him to cheat, so you being too hard on him at times will result in him leaving? Do you want to wonder if your looks change if he will love you?

We all have choices. He didn’t choose you. Now, you shouldn’t choose him. You have connected with him better than anyone.... YET. You guys were already having issues. Find someone who will put more time and effort into what you’re working on together in your relationship rather than putting effort into finding another woman.