I think that anger is not a real emotion, but rather a symptom of an underlying emotion.
Those emotions are pain, fear, or frustration.
In my experience, people often express pain, fear, or frustration, through a display of anger.
Not a FEELING of anger, but a DISPLAY of anger.
And I have noticed that I do not respond the same way to displays of anger, as I do to expressions of fear, frustration, or pain. That is to say that when people display anger toward me, or in my presence, I tend to put up walls, and distance myself, and protect myself.
When people express fear, frustration or pain, however, I tend to empathize, and draw closer to that person, rather than defend or protect. I suppose it would be good for me to work on realizing that when people display anger they really have some other underlying emotion, and I can still empathize, even though they are expressing anger. But that won't come naturally to me. I will need to work on that, if I want to make it so.
Why do people project anger when they really feel something else? I don't know. Pride maybe? The fear of looking weak? I don't know. But it creates a lot of dysfunction in the world, I think.