Agreed - I’d break it off with him. A decent person would have tried to help, but at the very least wouldn’t have blamed you for the glass getting broken. It was an accident, it happens! You’re not a child who should only be using cups in case you hurt yourself, either.
It sounds like he was purposely picking a fight with you and can’t even be honest with you about what he’s thinking now. Him following you to keep arguments going is also really concerning. He doesn’t respect your need to get some breathing space.