mia, hi, if I can ask: "How old are you two?" Sounds like he is very immature. And how can he think you are going out with someone else when he says so himself, even if he says he is "just saying that because he's mad"? Besides, after 6 years, if he is still so immature and still does not respect you enough to even trust you, I mean c-mon, he has no right to want you back. The only way to break his cycle of whining is if he goes to your parents' house where you are staying and talk it out with you & your parents.
Otherwise, the situation will get worse. If he does not give and start trusting you, there is no reason for you to come back to him. Stay with your parents for a few days and see how he acts. In this case, he should be the 1st one who should apologize to you and your parents, not you. Make him beg. If he is not man enough to admit he's wrong, then leave him. That will teach him a lesson and force him to see what he's missed.

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