you are the vendor and that they are the customer. Suck it up and gut it out. Prepare your arguments, and look for a better time to present them.
Some people use anger as a negotiating strategy. They use people's natural inclination to avoid confrontation to win disagreements. Some seek confrontation for its own sake. They may even disrespect you if you do not fight back. Such situations require delicacy and diplomacy. If you cannot disengage, and you feel that you will lose their respect if you don't fight back, then you must ratchet up the dialog gradually, always allowing them to cross each threshold of civility first.
Often in a confrontation, people realize that they are out of line, but they can't back down gracefully. Always try to leave your customer an "out" — a way of saving face in a confrontation. For example, give them a piece of information that they didn't have previously, so they can say "I didn't know that — it changes everything!"
There is a place for emotion in the workplace. However, expressing strong negative emotions in a public forum is usually counter-productive and frequently injurious to your career. If you have strong feelings about this, then...let me get back to you.