If I had an outburst like this towards one of my superiors at work, I'd be fired on the spot regardless if I apologized or not. I really don't see why this should be any different.

If you have this type of reaction to something, you are obviously reacting with emotions rather than clear thoughts. Voicing your opinion should be done in a completely civil environment. That fact that he says he won't be muzzled is pretty clear sign that he should be removed from his position.