The most important skill I've learned in my lifetime is not needing to have the last word. At some point, I realized that almost nobody is going to admit they're wrong in the middle of a discussion or argument. That's just not how humans work. Everyone wants the last word, especially when the disagreement is contentious. So say what you need to say, once. Then let the other person have the last word. It's okay. It doesn't mean anything. If you're right, they probably already know it, and over time they'll think about it and will change their mind. That's how humans actually work. And they will almost certainly never tell you, "You were right." That part you just have to let go of.