You're not wrong, but that's also not how people think in that situation.
The whole reason he cheated on her is because he is comfortable with her and likes being with her, he just also felt like he could get away with getting something on the side for nothing.
I've been on both sides of this, and from his side, you're feeling guilty, exposed, and like a piece of shit. You sit there and take your licks because you think you owe it to the person you cheated on. And in some ways, you do, and more.
The human brain isn't rational when it comes to this stuff. He's probably wanting to save/fix things and willing to sit through and endure punishment to keep the thing he's afraid he's about to lose forever. The thing that was good, except for this one aspect of it he got from someone else....
At least that's what's going through his head.
The truth is cheating is never excusable, always break up or end things first. Again, on both sides of this, it's a shitty, shitty thing to do and there's no excuse that is worth hurting the other person like this.