You have to realize that it is hard for people to admit that they are wrong or defeated, it's humiliating! Some teacher in an otherwise useless management training once taught me a neat little trick: offer a way for them to come over to your side without losing face.
Bad: "Just admit that my arguments are better, John!"
Good: "Hey John, do you think you can accept my view on this?"
Notice how the second version makes it very easy for John to say: "Yes, I can." You're not asking him to invalidate his own arguments, you're asking him to agree with you - which is far, far easier to do.
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