Most Helpful Guy
Seems clear your ex is both extremely immature and very capable of nursing an ill-conceived grudge, First thing to do would be to report his account to Facebook, and second thing would be to consider a restraining order. Yes, those orders can include social media/ third party harassment.
As for why he is doing this, it's hard to say for certain, but probably revolves around a "I can't believe that bitch dumped me" temper-tantrum.
Don't worry so much as to why. Do take positive steps to shut his online bullying down..1THIS IS NOT RELEVANT ANYMORE
Most Helpful Girl
As has been suggested, you should report his account and then block him. It's sad when ex-boyfriends turn into psychos and accuse you of things. I've been through something similar a couple of years ago with a guy who told everyone I was stalking him. Like you, I was concerned that people would believe him. But in the end, those people that believe him are going to be those people who don't know you, and what those people believe doesn't matter at all. I don't know why your ex-boyfriend does it. It could be his hurt ego, it could be that he's scared you're going to tell people the truth about him (that he flirted with other girls, that he was leading you on, etc.) and he's trying to portray you as this crazy woman just in case you do tell people the truth. I found out months later that my ex-boyfriend did it because he found a new girl and I assume he was scared that she'd find out that in the beginning when he started seeing her, he was still sending me rather intimate messages. So in my case, I guess it was the "let's paint her as this crazy psycho so that if things surface, nobody will believe her" thing.1THIS IS NOT RELEVANT ANYMORE