Psalm 39 has an amazing description of what I call "amygdala overload." You hold your tongue when something makes you angry, and bottle it up. You're silent to no avail; your distress grows worse, Then your "heart becomes hot within." You muse over all the things you should have said, over all the things you'll say when you get another chance. While you muse, the fire burns, and then you speak. THAT can't be good. I've been there. One of the great things about the Bible is that it's written by humans. It is relatable because it reflects fallen, human emotions.
I think the Psalmist realizes how bad this speech from a place of anger can be. In verse 8, it says, "Deliver me from all my transgressions." Before, he was ruminating about someone else and that was making him angrier and angrier. Now he is thinking about his own part in it. This is the move Jesus was calling for in Sunday's passage in Luke: stop thinking about whether other people were sinful or not, and focus on your own repentance.
Jeremiah points out that God can get angry, too. 11:17 says "The Lord . . . has pronounced evil against you because of the evil that the house of Israel and the house of Judah have done, provoking me to anger." I absolutely believe that God feels emotions: anger, in this case, but also sympathy and love. Jesus became human and felt anger and was tempted in every way that we are, yet without sin. In Sunday's Luke lesson (13:1-9), the owner of the fig tree seemed angry and Jesus told this story just after he told people that unless they repent, they will perish just like the victims of those tragedies.
Paul gives a different slant. It is not God's anger that should lead us to repentance, but God's kindness: "Do you despise the riches of his kindness and forbearance and patience? Do you not realize that God’s kindness is meant to lead you to repentance?" Ultimately we have a kind and patient God, but Paul also points out that we have an impartial God. Impartiality is a good thing if you're on the short end of an injustice, but I think that for most of us, we don't really want an impartial judge. We'd be condemned. The thing that kindles God's anger in Paul is not the things we should be repenting of, but instead refusing to repent at all--impenitence itself. "By your hard and impenitent heart you are storing up wrath for yourself on the day of wrath, when God’s righteous judgment will be revealed."
One last thing: penitence, repentance, self-conviction--these things sound bad, but they're really very good. It is an act of kindness by God that God leads us to repentance. "To those who by patiently doing good seek for glory and honor and immortality, he will give eternal life." Part of doing good is self-reflection so that we know when we're doing bad, turn to the Lord, change our ways and then can do good. That's a process that's worth celebrating at every step along the way, including the repentance part. So penitence, repentance, self-conviction--these things are good things. Not doing them means not having an opportunity to get better, and we all want to get better.