Offer to bet him money about the outcome of some real world event that is contingent on the way he is claiming that things are
IDK how you can apply that to AI; that’s not the best one. But you can bet that there are no workers dying of heatstroke in Amazon-supplier warehouses. You can bet him that Trump has agreed to honor the results of the election. Etc etc.
It’s very easy to just make statements at each other. If you offer to back up your statements, then he can either refuse (in which case it’ll be harder for him to say he’s definitely right and you’re definitely wrong), or agree and then one or the other of you will learn something.
It’s up to you. You can also just let it go. But if you want to prove him wrong it is easier to do with questions and real-world actions than it is by coming up with the perfect statements. As you’ve discovered, he’s not obligated to react to statements any way other than how he’s decided to react to them.