I don't think I'd want to spending too much time arguing over most words, especially not the word anger. I definitely wouldn't get upset about it.
Whatever you want to call it, I just don't think we can deny that there are times when it is biblically appropriate, right, for our adrenaline to start pumping because something is wrong, times when it is right for us to be disappointed, bothered, and even upset…all at once.
I say that for a couple of reasons.
They may not all carry equal weight, and they are pretty much the product of about 5 minutes thought, but put them all together and at least I'm convinced there's such a thing as righteous anger.
1.) The Bible says "Be angry and do not sin…" which seems to indicate to me that you can be angry and not sin. Commenting on this verse, John Stott writes, " This verse recognizes that there is such a thing as Christian anger, and too few Christians either feel or express it. Indeed, when we fail to do so, we deny God, damage ourselves, and encourage the spread of evil" (The Message of Ephesians, p.185).
2.) There were times when Jesus became angry. (For one example see Mark 3:1-6) Jesus perfectly fulfilled the law of God which means he didn't only not do wrong, he always did right. That seems to say, becoming angry in those situations was the biblically appropriate response. (For more on this, I'd suggest B.B. Warfield's "The Emotional Life of Our Lord". After many Scriptural proofs of Christ's righteous anger, he writes, "Jesus’ anger is not merely the seamy side of his pity; it is the righteous reaction of his moral sense in the presence of evil. But Jesus burned with anger against the wrongs he met with in his journey through human life as truly as he melted with pity at the sight of the world’s misery: and it was out of these two emotions that his actual mercy proceeded.")
3.) Although God is slow to anger, He does become angry. Nahum 1, Psalm 2 are examples. If God is holy, never does wrong and becomes angry…anger in and of itself, doesn't seem to be sinful.
4.) Every other emotion that I can think of has a biblically legitimate place in our lives. I can't think of another emotion that doesn't have a place. Fear, can be right and wrong. Sorrow, can be right and wrong. I'm not sure I'd call desire an emotion, but desire can be right and wrong. This isn't really a biblical proof, but at the least, it would be strange that there would be this one emotion that can only be wrong.
I'm not saying righteous anger is common. I think alot of what we call righteous anger isn't. I'm simply saying there is such a thing.
I like how John Piper puts it, "Most human anger is bad. Most of it arises from proud self-asserting hearts which feel like their rights have been denied. And most of it aims at revenge. If we have been put down we will make sure they get their comeuppance. So James says, "The anger of man does not work the righteousness of God" (1:19).
But there is a rare holy anger that comes from and aims at the righteousness of God. The man or woman who is filled with the Spirit will be humble and gentle and slow to speak. They will sit in silence and prayer and soul-searching for perhaps twenty-nine chapters of confused conversation. But there will come a point when the self-justification of man and the accusation of God become unbearable to their holy sentiments and they will get angry. The mark of righteous anger is that it is triggered by the belittling of God not the belittling of ourselves."
Matthew Henry agrees, "Though anger in itself is not sinful yet there is the upmost danger of its becoming so if it be not carefully watched and speedily suppressed. And therefore, though anger may come into the bosom of a wise man, it rests only in the bosom of fools…"