He admitted he would never have told me as he didn't want to hurt me,
So he reasons you knowing about it is the thing which would hurt you then.
So as long as you don't know, you won't be hurt, right? So nice of him to try to spare your feelings.
What else hasn't he told you about because it would hurt you?
His thinking and reasoning is somewhat warped i'd say. Perhaps not do the thing that would hurt you in the first place? At the very least not do it again! I'll bet it was more than twice. He has has to admit what he did because you found out. He'll be admitting to the absolute bare minimum.
He has already told you he won't tell you things that he does, so he doesn't 'hurt' you.
Who the hell does he think he is? He is basically telling you he will take away any choice you have in the matter to be with someone who cheats by simply not allowing you to know about it.
HE has decided not to allow you to make that decision.
HE has decided to make that decision for you because if he doesn't want to risk you choosing to leave him.
He wasn't protecting you, OP. He was protecting himself.
And now you know, and have a choice in the matter, he is throwing in the depression card. Making sure you know it wasn't his fault at all. It was the depression, the drink, the friend making him do those things. Of course he is full of self loathing. He has been caught. Its probably more embarrassment that you've caught him out, than self disgust. If he was so disgusted with himself, why go back and do it again (and again, and again, and again?)
I'm sorry to say, based on that one statement, he has told you who he is. There will be so much more you are blissfully unaware of.