Arguing with another being is bound to happen with someone over a given time frame. The important focus is how to deal with the conflict without harm. Sure there are times in frustration where you want to just fight and get it over with, however think about if it is really worth it. Is that conflict really worth your blood, sweat, and tears? Knowing when to fight and not to fight is a big step in becoming a better person.
Make sure to remain calm at all costs. Not only does this make you the more mature being, but also shows you have more self-control. Who cares what last word he/she says? Will you see him/her again if he's a stranger? Probably not.
Never look into their eyes. This can only fuel more anger, however it can backfire if they find not looking at their eyes is disrespectful, so I'd advise to be careful on this.
Be the smarter being. Stay focused and analyze the person while they're rambling about how you look bad, how you are weak, or something else irrelevant to the situation (usually).
Stay off to an angle of the person. Never stand directly in front of them. This exerts all of their frustration and maddening energy directly towards you. Angling off allows the energy to flow away. This falls directly in line with keeping a distance from the person at all costs. If they come in, assert that they need to keep their distance, or slightly back up, but don't back up too much, as this will portray weakness to the other person.
While some may read this and think of the person doing this is the lesser man, think of it optimistically and realize the bigger man is one who does an action that results in no harm to either party. This might be slightly embarrassing, but it is definitely more worthwhile as the next day you won't be feeling the soreness from the actions dealt. Myself, training in certain Martial Arts, I definitely lean towards not fighting. If what you're striving for is efficiency, this is one of those principles. What slows you down tomorrow because of today will not benefit you, but only slow you down.
If the person starts coming to you in a forceful attack manner in any way, counter immediately and be the first to finish. Efficiency is key, there is no point in dragging on a fight. However, be verbal to always try and stop the fight first after the first blow. If it continues, then finish it and walk away.
Now while I'm not trying to tell people how to deal with conflicts, I feel this is the best approach in advice towards those specific situations. Always be forgiving, and never let the conflict get out of hand. To stay in control is to stay in power, and that is most important in these types of conflicts.
I bring this post up because it is an event that recently happened to me this weekend. I knew the person was not going to do anything just by analyzing, but always stayed in control of the outcome. In the end I will probably never see the person again, and am not feeling the consequences of that event now. I'll bring in some experiences like this occasionally to fuel some posts, but I thought it was a good idea to touch on. Anyway, hope everyone's weekend was a blast! Stay positive.