This is true and also very important. One thing I find helpful to remember: if someone comes at me angry about something I said, however innocent my intent, they may well have cause. In that case my first priority must be to find out what it was I did wrong so I won't repeat it. And one cannot always expect people to behave reasonably when one has hurt them. In the best cases I've been able to work out what I did wrong and at the same time conveyed my apologies. That often goes a long way towards better communication afterwards.
Another point to remember: it is not often helpful to tell someone not to be angry. If they are actually communicating in good faith, they will be angry for cause and in that case the solution is to discover what caused the anger and hopefully alleviate it. If they are not communicating in good faith -- this is unfortunately also possible -- no appeal to their better nature will work in any event. And most importantly of all, there are those who simply use anger as an excuse to dismiss the angry person's argument. This is a much-loved tactic of those who wish to silence victims of (for example) misogyny, homophobia, transphobia and racism. It is called tone policing and works like this: if you are angry, your argument is invalid, if you are not angry, you have no reason to complain.
The above is the ideal and unfortunately I cannot always live up to it. For one thing, I have a temper of my own and I cannot always control it. But for exactly that reason I try to remember that the anger of the other person may very well be valid and should be respected.