Anger, in my experience, is not an emotion: it is a direct refutation to an emotion you do not, or can not, allow yourself to feel. Scratch the angry person and you will find fear, hurt and/or helplessness.

It is interesting, and instructive, that you begin and end your excellent piece with the description of a child in mid-tantrum. The angry child says NO as loudly and as physically as he can. It's not the saying NO that is, per se, the problem: it's that which he is saying NO to... that's the problem.