At some point a customer is going to disagree with you, oppose you, or argue with you. There’s a right way and a wrong way to have a disagreement with a customer.
Be Prepared
The best way to successfully have a difficult conversation is to avoid creating tension. The way you do that is to be ready and aware when the conversation is heading in the wrong direction–you don’t want to add to the tension.
Notice when your customer is talking louder or faster. Watch when he repeatedly points his finger at you. You have a problem when his face gets redder and he has more animated facial expressions. Stop thinking about your response when you see these signs and start listening very, very well.