I had a job with angry parents! It was part of the job training to learn how to deal with this (lucky me!). I have also learned that people are angry for all sorts of reasons. Some people are angry from way back and when they get triggered by customer service ALL the anger comes out.

What I learned with my training is to stay calm no matter what. It really works. I still use it today even though I don't work in that job anymore. No one can remain angry when the person that they are talking with is calm. I called the road dept. once to make a complaint. The guy went off right away. I ignored it and remained calm and was actually extra nice. He would calm down and then when the subject would change he would go off again. The whole 10 minute conversation went 1) he went off, 2) I remained calm and nice, 3) he calmed down, and the conversation took about 4 cycles of this.

I don't even get too rattled with this stuff, in even person. The other person is not going to physically attack me so I have nothing to fear except their anger. People who fear anger have a history of a dealing with a parent's anger (I have yet to come across anyone where this wasn't the case). You can work your way back through this stuff.