He is being manipulative and emotionally abusive and you do not need to put up with it or prove yourself to him. Either he trusts you or he doesn't. Unwarranted jealousy usually comes from a place of them actually being the one that is untrustworthy or self esteem issues. Life is too short to be accused of things you aren't doing or that aren't true. He either needs to seek help for his insecurities or it should be time for you to rethink the relationship.