The verbal root of this word is אלף (A.L.Ph, Strong's #502) and means "learn," but more literally, to learn through association, as can be seen in the following verse.From http://kolobiv.blogspot.com/2008/09/sampling-school-of-prophets.html
Make no friendship with a man that is given to anger; And with a wrathful man thou shalt not go: Lest thou learn this ways, And get a snare to thy soul. (ASV, Proverbs 22:25)
So much anger and wrath is learned from the wrathful and angry. The Bible has a great deal of good to warn us against when it warns us not to learn from them. The entire ADR movement is really a movement towards being peacemakers and away from wrath.
As an aside, I once was in a class where the instructor asked us what was the greatest revenge we could seek. A friend of mine answered that it was to let people remain in their ignorance so that they did not repent or change, but remained essentially damned by their lack of knowledge. Being wrathful does that to people, it blocks self-knowledge and the ability to change.