School administrators are routinely required to deal with people who are upset about a teacher, their tax bill, a policy, etc. and we, having been trained to be logical, often attempt to calm them by presenting them with facts and logic.  But it almost never works.  In fact, it often makes them even angrier.  The reason is that they are operating on an emotional level and you are on the rational level.  You have to deal with a problem at the same level at which the person brought it to you.  If a person is upset, you must deal with their emotions by being empathetic, showing understanding, etc.  You don’t have to agree with them but you must respond to them at the level where they are.  But logic almost never assuages a person who is upset, i.e. logic never trumps emotion.  Wait until they have thoroughly ventilated and calmed down and then ask "what would you like me to do?"  Often the answer is "nothing" because they just needed to ventilate.  But if they do want something, try to give them at least one "yes" answer before you can ease into the facts and talk about policy, behavior, etc.  But never start the problem-solving phase until they get beyond their emotional phase!  (See:  "Never Interrupt a Tirade")