Two things are wrong with a fool’s wrath at the same time. As many point out, even a righteous man can overreact, and his anger can be a form of madness which is had to bear without losing respect for the man, but at least we can see some justification for his strong reaction, but a fool has no such mitigation.
Let believers not be intimidated by unrighteous anger, as if it gave any evidence that the fool had a righteous cause. Though the fool uses anger as a way of justifying himself, his anger is a false construction, which God will tear down by a much great and more final righteous anger. Let the righteous man not be shifted from his righteous stance, or made to doubt the truth of his cause by the fool’s anger. It is a smokescreen designed to hide his sin. God’s true standards must prevail and every argument that lifts itself up against the knowledge of God will be cast down.