You can't win an argument because even if you win, you lose. You have made your opponent feel inferior. You have hurt his pride. He will resent your triumph.
Lincoln said, "No man who is resolved to make the most of himself can spare time for personal contention. Still less can he afford to take the consequences, including the [venting] of his temper and the loss of self-control. Yield larger things to which you show no more than equal rights; and yield lesser ones though clearly your own. Better give your path to a dog than be bitten by him in contesting for the right. Even killing the dog would not cure the bite."
Some suggestions on how to keep a disagreement from becoming an argument:
You can tell people they are wrong by a look or an intonation or a gesture just as eloquently as you can in words - and if you tell them that they are wrong, do you make them want to agree with you? Never! For you have struck a direct blow at their intelligence, judgement, pride, and self- respect. That will make them want to strike back. But it will never make them want to change their mind.
If a person makes a statement that you think is wrong - even if you know it is wrong, say, "Well, now, look. I thought otherwise, but I may be wrong. I frequently am. And if I am wrong, I want to put it right. Let's examine the facts."
Carl Rogers said: "Our first reaction to most ... statements is an evaluation or judgement, rather than an understanding of it. ... Our tendency is almost immediately to feel, "that's right," or "that's stupid," "that's abnormal," that's unreasonable," "that's incorrect," "that's not nice." Very rarely do we permit ourselves to understand precisely what the meaning of the statements is to the other person."
Ben Franklin said: "I made it a rule to forbear all direct contradiction to the sentiment of others, and all positive assertion of my own. I even forbade myself the use of every word or expression that [implied] a fixed opinion, such as certainly, undoubtedly, etc. [clearly, obviously, evident, surely], and I adopted, instead of them, I conceive, I apprehend, or I imagine, a thing to be so or so, or it appears so to me. ... When confronted with another person's error, begin your answer by saying the certain cases or circumstances where his opinion would be right, but in the present case, there appears or seems to be some differences."