I have to say, I wondered from your first post if he'd met someone else.
His behaviour during and after the break-up could be argued to be consistent with someone who is bouncing between a couple people and not being totally honest. This is why I asked what the argument was about.
However, as you said, it is actually not that important anymore. He decided he didn't want to continue the relationship, which hurts, but is all the reason you need not to contact him now. No good will come of it.