"One of us is wrong...
and it's not me."
That's the way every single conflict begins. Of course it does, because if it didn't, it wouldn't be a conflict, would it?
So, given that the other person is sure you're wrong, what are you going to do about it? Pointing out that they're wrong doesn't help, because now you've said the second thing in a row that your partner/customer/prospect/adversary doesn't believe is true.
The thing that's worth addressing has nothing much to do with the matter at hand, and everything to do with building credibility, attention and respect. Only then do you have a chance to educate and eventually persuade.
We cure disagreements by building a bridge of mutual respect first, a bridge that permits education or dialogue or learning. When you burn that bridge, you've ensured nothing but conflict.