I am currently reading through the classic 1930's writings of Dale Carnegie's How to Win Friends and Influence People. Still a classic, and still pretty much relevant today, which struck me in the same awe as my earlier encounter with Elbert Hubbard's works. If you haven't read this book, please get a copy soon!
I am quoting some tips from Part Three, Chapter One on how to keep a disagreement from becoming an argument (that Carnegie himself sourced from an article in Bits and Pieces, published by The Economics Press, Fairfield, N.J.):
Welcome the disagreement
Remember the slogan, "When two partners always agree, one of them is not necessary." If there is some point you haven't thought about, be thankful if it is brought to your attention. Perhaps this disagreement is your opportunity to be corrected before you make a serious mistake.
Distrust your first instinctive impression
Our first natural reaction in a disagreeable situation is to be defensive. Be careful. Keep calm and watch out for your first reaction. It may be you at your worst, not your best.
Control your temper
Remember, you can measure the size of a person by what makes him or her angry.
Give your opponents a chance to talk. Let them finish. Do not resist, defend or debate. This only raises barriers. Try to build bridges of understanding. Don't build higher barriers of misunderstanding.
Look for areas of agreement
When you have heard your opponents out, dwell first on the points and areas on which you agree.
Look for areas where you can admit error and say so. Apologise for your mistakes. It will help disarm your opponents and reduce defensiveness.
Promise to think over your opponent's ideas and study them carefully
And mean it. Your opponents may be right. It is a lot easier at this stage to agree to think about their points than to move rapidly ahead and find yourself in a position where your opponents can say: "We tried to tell you, but you wouldn't listen."
Thank your opponents sincerely for their interest
Anyone who takes the time to disagree with you is interested in the same things you are. Think of them as people who really want to help you, and you may turn your opponents into friends.
Postpone action to give both sides time to think through the problem
Suggest that a new meeting be held later that day or the next day, when all the facts may be brought to bear. In preparation for this meeting, ask yourself some hard questions: Could my opponents be right? Partly right? Is there truth or merit in their position or argument? Is my reaction one that will relieve the problem, or will it just relieve any frustration? Will my reaction drive my opponents further away or draw them closer to me? Will my reaction elevate the estimation good people have of me? Will I win or lose? What price will I have to pay if I win? If I am quiet about it, will the disagreement blow over? Is this difficult situation an opportunity for me?