Anger makes people forget logic and reason. They go into a whole different zone altogether. Most people start off calmly in dealing with an angry person, but eventually they get sucked into a slanging match with the person in question. Not good that - in fact in most cases, its what the angry person wants. They are comfortable in that zone. Perhaps, they've been there and done that much more than you have. So, they are much more experienced than you in getting into arguments and fights, etc. Would you really want to compete with such a person? Can you hope to win either an argument or a fight with such a person? The honest answer to that would be a firm NO.
Here's what you should be doing instead of getting into an argument/fight with an angry person. First, you need to stay calm at all times. This is important. You can't hope to get the desired result, if you yourself get sucked into it. That would only exacerbate the situation and make it more volatile, possibly dangerous. The accusations may sting you, hurt you, you many want to try to provide counter facts and try to prove them wrong - but is it really worth it? Highly unlikely - facts will only work with a logical person, who is in control of himself/herself. The best way is to stay calm and ignore whatever this person is saying. You could say to this person a sentence of two to the effect "I am not going to argue with you on this. You can go on saying what you want." OR "I won't dignify that with a response." The goal is to let the person go on and make himself/herself look like a fool - that they really are. You could then just walk away from the scene. You are not a coward in doing that. What you are in fact doing is nipping a potentially deadly situation in the bud.
If the anger is not directed at you, but at someone else and you are playing the mediator - then you would have to be a little bit more proactive. You need to get in between the two individuals having the argument and get them a fair distance away from the immediate area of confrontation. Ensure that there is no sustained eye contact between them. You could then divert the conversation to something else to take the sting out of the argument. For example, you could remind them of a chore that they had to perform and something else that they were supposed to have been doing.
Its worth remembering that many of these arguments start small, perhaps over something totally small and insignificant. However, many of these turn into situations where people lose their lives. People do a lot of stupid things in anger - not all of them are silly - you could get killed in one of these angry confrontations.
