If you happen to find yourself in front of a conflict, the only good, right and noble thing is to try to make it smaller, to push it inward with both your hands until it is the size of a pebble. Then, you must toss it away.
And if you cannot do this, if the people involved are entirely irrational, and if not irrational, then, I reckon, deaf to the sound of reason? Then, you must remove yourself from the situation. It is natural to want to add fuel to the fire and feed it until it consumes everything around us; there is a primal instinct in all of us to do this, but it takes a person of character to ignore the urge. And what if you, yourself, are in the ring? Even then, you must try to avoid all conflict. I cannot recall a situation where giving into my urge to deck someone or to say something harsh brought with it an appreciable result. I hope you remember this if you have never been in a fight. But I reckon all of us have been in an argument or two.
It is impossible to be a person without disagreement. It is, however, not only possible but quite common for disagreements to grow into animosity for no other reason but because, like a virus, they were not contained. Most believe it to be opportunity. It is indeed an opportunity. It is an opportunity to display how small of a person you could be if given the chance. To say I am immune to this would be a lie, and I have walked away with many arguments and fights only to lose a friend or worse, if an outcome as abysmal as losing a friend exists.
There are not many correct things in life, and it may all be chalked up to opinion, the countless differences, and the many manifestations of personalities, but there are some without ambiguity.
To apologise, if the situation demands it, regardless of how big or small the error is one of them. And if an apology, whether in truth or as a white lie, is too much to ask of you in the spur of the moment, then to stay your tongue, to not utter a word, to stand where you are until you can leave, and then, to go without the softest sound still, says more than anything clever or poisonous you can imagine. To remember this shows the mettle of a person. Nothing else comes close.