Not “who’s right?” but, “what’s right?” Which matters more?
When talking to someone and trying to convince them of something, what matters is that they agree with the idea, not the person.
Often times people will agree with you to shut you up. What the goal of persuasion should be then is that the idea itself has to be confirmed.
If you get them to say THAT is right instead of YOU are right, you’re on a better path to seeing a change occur.