Sometimes we forget the old (but true) cliche:
Rule #1: The customer is always right.
Rule #2: If the customer is wrong, see Rule #1
It is easy to focus on metrics, teams, marketing, image, sales quotas, strategic plans, stock price, water-cooler gossip, and the lunch hour. But often we forget why we are at work in the first place.
Without the customer, everything else stops. Sometimes customers are difficult. Often they are annoying. Regularly they are unrealistically demanding. And yes, on occasion the customer is wrong.
But when they are wrong, you cannot dig your feet in with the hopes that you will "win" and educate them on the error of their ways. To beat the customer is to lose the customer, and all the goodwill.
Your relationship with your customer should never be compared to a boxing match. If you feel you are going twelve rounds and hoping for a TKO, you need to step back and take the fall.
Too many people have forgotten that. They want so badly to be right, that they alienate customers along the way. If this has not happened to you recently, then consider yourself lucky.
(On the other hand, yes, there are times when you should "fire" a client when they are not a good fit with your long term goals. But you do that in a professional manner....not by beating them to a pulp).
Have A Great Day.