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I think you're justified in breaking up with him, but I fail to understand why you so adamantly refuse to tell him why you did so.
It would take you less than a minute to text "I dumped you because I found out you were flirting with other girls." Simple. There is a small chance that it was a misunderstanding, in which case you could salvage your relationship. Even if that's not the case, you would both get closure. If he knew why you ended things, he might even change his ways--so he doesn't hurt any other girls in the future.
You have much to gain and little to lose. The only reason not to give him an explanation is pettiness. He is absolutely in the wrong, but that doesn't mean you need to be childish too.
Is this for real flirting or online? I personally think all this online sexting is bull and means nothing until you meet. I don't have a belief that online crap is nothing real. But I do agree that social norms like respecting loyalty is important. i guess that if it was
online was it real.