In this case, you are choosing to prove you are right and he is wrong. It isn't going to change him. You can't prove an abusive manipulator wrong no matter how right you are.

You'll feel vindicated for a few days without a doubt, but it won't last and he will find a way to use anything you've said to hurt you. I've divorced someone who tried this. The game stopped when I stopped playing it. And even then it took a few years for the ex to realize I wasn't participating anymore.

As long as you play his game, he will find a way to win and have power over you. I'm not saying this to hurt you and it's not judgement. It's an abuse survivor's advice to stop playing his game to stop the cycle.