The Bible doesn't say that should never be angry. Did you know that Jesus, the perfect man, the Son of God, drove the greedy money changers out of the temple (John 2:14-15). We are expected to be angry at oppression, injustice in the world, at blatant cruelty - in other words, at sin.
The anger most of us feel is when we're being slighted, ignored, insulted? It's more like pride and ego that lead to most of our anger? This kind of anger the Bible does warns us against.
So then, my beloved brethren, let every man be swift to hear, slow to speak, slow to wrath; for the wrath of man does not produce the righteousness of God. James 1:19-20 (NKJV)
Do not hasten in your spirit to be angry, For anger rests in the bosom of fools. Ecclesiastes 7:9 (NKJV)
Beloved, do not avenge yourselves, but rather give place to wrath; for it is written, "Vengeance is Mine, I will repay," says the Lord. Therefore "If your enemy is hungry, feed him; If he is thirsty, give him a drink; For in so doing you will heap coals of fire on his head." Do not be overcome by evil, but overcome evil with good. Romans 12:19-21 (NKJV)
A soft answer turns away wrath, But a harsh word stirs up anger. Proverbs 15:1 (NKJV)
Cease from anger, and forsake wrath; Do not fret--it only causes harm. Psalms 37:8 (NKJV)
A fool's wrath is known at once, But a prudent man covers shame. Proverbs 12:16 (NKJV)
Go from the presence of a foolish man, When you do not perceive in him the lips of knowledge. Proverbs 14:7 (NKJV)
Make no friendship with an angry man, And with a furious man do not go, Lest you learn his ways And set a snare for your soul. Proverbs 22:24-25 (NKJV)
An angry man stirs up strife, And a furious man abounds in transgression. Proverbs 29:22 (NKJV)
Scoffers set a city aflame, But wise men turn away wrath. Proverbs 29:8 (NKJV)
"But I say to you that whoever is angry with his brother without a cause shall be in danger of the judgment. And whoever says to his brother, 'Raca!' shall be in danger of the council. But whoever says, 'You fool!' shall be in danger of hell fire. Matt 5:22 (NKJV)
"Be angry, and do not sin": do not let the sun go down on your wrath, Eph 4:26 (NKJV)
But now you yourselves are to put off all these: anger, wrath, malice, blasphemy, filthy language out of your mouth. Do not lie to one another, since you have put off the old man with his deeds, and have put on the new man who is renewed in knowledge according to the image of Him who created him, Col 3:8-10 (NKJV)