Seriously, fighting will just make the situation worse and you could lose the customer or even lose many customers.
Understanding where that anger comes from will help you avoid being sucked into a fight with a customer. Psychologists say that anger is not a primary emotion. Anger usually comes from fear or a feeling of hurt. Once you realize that yelling and strong words come from fear or hurt then you can figure out how to calm that customer down.
If a friend came to you upset and in tears, what would you do? Would you yell at them or kick them? No, you would sit there and listen to them and validate them. Even if they aren't right in what they are saying, they just want to be heard and validated. Try to remember this when dealing with an angry customer.
So if you remember that anger is a fight or flight emotion and that fighting back will not work, you will be able to handle the angry customer in way that is not confrontational. Remember their anger is not personal, they are afraid or hurt.
When you listen, validate, and talk calmly, and once the customer has calmed down, you can resolve the problem and calm their emotional state. When you take care of their emotional need, you will form a bond to that customer that will be hard to break. Their confidence and trust in you will grow tremendously and you just may have that customer for life. All it takes is a little understanding and you can turn an angry client into a loyal customer.