It's easy to scoff at the old saying, "the customer is always right." As anyone who has worked retail knows from experience, the customer can be magnificently wrong, as well as ignorant, unreasonable, rude, even abusive.
So the saying shouldn't be taken literally, but that doesn't mean it has no value. Sayings are often intentionally exaggerated in order to leave a memorable impression and to make a point. And this one makes an important one.
The deeper meaning is that, for your own career success, satisfying the customer is more important than correcting the customer.
The classic book How to Win Friends and Influence People by Dale Carnegie includes a chapter called "You can't win an argument." In it, Carnegie tells a story about a salesperson named Pat who had a habit of arguing with customers:
…he came to me because he had been trying, without much success, to sell trucks. A little questioning brought out the fact that he was continually scrapping with and antagonizing the very people he was trying to do business with. If a prospect said anything derogatory about the trucks he was selling, Pat saw red and was right at the customer's throat. Pat won a lot of arguments in those days. As he said to me afterward, "I often walked out of an office saying, 'I told that bird something.' Sure I had told him something, but I hadn't sold him anything."
Carnegie also quotes an old poem:
Here lies the body of William Jay,
Who died maintaining his right of way -
He was right, dead right, as he sped along,
But he's just as dead as if he were wrong.
A marriage counselor once asked an argumentative husband: "Do you want to be right or do you want to be happy?" Similarly, in our careers, we should ask ourselves, "Do I want to be right or do I want to be successful?"
This is not to say that it never makes sense to correct a customer on a point of fact, that you should give in to unreasonable demands, or that you should beg for forgiveness whenever a customer is dissatisfied.
It's just a matter of keeping your primary goals in mind.
You probably want to earn money and advance your career prospects. The most effective way to do both is to help your employers achieve their business goals. Two of the most important goals for any business are to make sales in the short run and to maximize customer goodwill in the long run (which leads to future sales). Those are your top two objectives if you want to succeed in a customer service job.
So when you feel the urge to argue with a customer, asks yourself: "does this promote sales and/or customer goodwill?" That's a great question to ask, because it's basically the same as asking: "does this advance my career goals"?
If the answer is no, then it's just a matter of deciding whether you'd rather be right or successful.