| From where I work we are allowed to reason with customers who are unreasonable (tech support) even if we get angry too, as long as we don't cross the line. If he asks for a supervisor, try to deescalate, if that doesn't work might as well give it to him, your supervisor will know anyway.
Focus on what you can do, not what you can't. If you can't give him what he wants, look for an option closest to it.
This won't always work though. There really are "Impossible Customers" sometimes. |