Only God's anger is righteous. Jesus was a man, like us. (also not like us, being begotten of God, but you understand what I'm saying)

We are not to be angry, because we are not gods ourselves and cannot judge with our own judgment, only God's judgment. All we can do is discern evil, and forgive. That's not to say we can't take action like flip tables either, just not out of anger. Personally, I interpreted that as Jesus making a point about wrongdoing, in the same way that you might condemn someone's actions or rebuke them without necessarily feeling anger towards them. I might take a drunk's beer and smash the bottle on the ground, or destroy a junkie's needle, and not feel strongly about it one way or another. I just see that something needs to be done and do it.

Hate is the opposite of love, and anger is only another word for hatred. People like to tone down words to make them more palatable. Like you might see "resentful" or "bitter" instead of "angry" or "hateful", but the spirit is the same.

Ephesians 4:31-32 is clear imo:

Let all bitterness, and wrath, and anger, and clamour, and evil speaking, be put away from you, with all malice:

And be ye kind one to another, tenderhearted, forgiving one another, even as God for Christ's sake hath forgiven you.