The break-up could have been a misunderstanding. I still wouldn't see it as cheating, even if it were.

However, this guy sounds emotionally manipulative, so my best guess says that you really were broken up.

As for the relationship in general, if your only reason for staying would be his threats, then that's even more of a reason to get out. Things sound pretty messed up. If you want to fix them, he's got to be open to that too. Most people aren't really willing to change though. You have every right to move on with your life though, and really, that would be my decision. If you'd been together forever, had serious ties, were engaged, had kids, or this behavior was sudden; then I'd look into the options more closely. As it is? Run.. before you can't get away so easily.