Dale Carnegie's How to Win Friends and Influence People. One of the chapters is titled "You Can't Win an Argument," in which Carnegie writes:
Nine times out of ten, an argument ends with each of the contestants more firmly convinced than ever that he is absolutely right.
You can’t win an argument. You can’t because if you lose it, you lose it; and if you win it, you lose it. Why? Well, suppose you triumph over the other man and shoot his argument full of holes and prove that he is non compos mentis (not sane or in one's right mind). Then what? You will feel fine. But what about him? You have made him feel inferior. You have hurt his pride. He will resent your triumph. And -"A man convinced against his will, Is of the same opinion still."