This means you can be angry and not sin! True enough, because Jesus Himself, who was sinless, got angry (see Matthew 21:12) God got angry a lot because of the Israelites’ disobedience (see the Old Testament) There is such a thing as righteous anger. But more often than not, the anger we experience everyday isn’t this kind.
When you get into an argument with someone, check your heart. Do you refuse to forgive because your pride was hurt? Learn to humble yourself. Forgive unceasingly, just as Jesus has forgiven you countless of times. Don’t stay angry! Anger destroys you more than it destroys the other person. And learn how to say sorry when you know it was your fault! :)