Hi. Sorry to hear that. It depend of the nature of the "mess up", how often this happened before. It also depend that the accumulation of many other small details unrelated to the current incident may have given inertia to his current decision.
As to why he go to dating site already, a good thing is that it mean he was not having some kind of affair and got the other women right away. The reason why he does this is unknown for now. Many man NEED a women in the house to do some things (some can't cook to save their live), some can't stand being alone. Ask yourself what you bring to him he can't do by himself and try to win him back that way.