read part 1). To understand, we need to look below the surface.
You have heard that it was said to those of old, "You shall not murder; and whoever murders will be liable to judgement." But I say to you that everyone who is angry with his brother will be liable to judgement; whoever insults his brother will be liable to the council and whoever says "you fool" will be liable to the fire of hell. So if you are offering your gift at the altar and there remember that your brother has something against you, leave your gift there before the altar and go. First be reconciled to your brother, and then come and offer your gift. Come to terms quickly with your accuser while you are going with him to court, lest your accuser hand you over to the judge and the judge to the guard, and you be put in prison. Truly I say to you, you will never get out until you pay the last penny
Not being a murderer is often our favourite way of justifying ourselves. Start talking about sin and sooner or later someone will say "well, at least I haven't killed anyone". Jesus offends all of us when he says that anyone who is angry is guilty of the same sin - which makes all of us guilty.
This is not about all anger because Jesus himself got angry. But our anger is rarely righteous, it is much more likely to be self-centered - someone said something we didn't like, someone didn't treat us in the way we thought we should be treated etc.
there is a place for burning with anger at sin and injustice. Our problem is that we burn with indignation and anger, not at sin and injustice, but at offense to ourselves. In none of the cases in which Jesus became angry was his personal ego wrapped up in the issue... Let us admit it - by and large we are quick to be angry when we are personally affronted and offended, and slow to be angry when sin and injustice multiply in other areas.
We are guilty of this anger and are in the same position as the murder before God, without excuse. But, while our anger is selfish, Jesus' anger was selfless. He was angry with our sin and dealt with it on the cross. That sets us free, we no longer need to be enslaved to the selfish anger that bears grudges and gets offended.
While we may recognise this selfish anger in ourselves, we often feel like it's alright to hold onto it as long as it is internal and we don't act on it, or at least keep our angry acts to a minimum. But the person who holds a grudge and faithfully attends church, gives financially and never misses a bible study has not offset the anger in their heart. Jesus advises working for reconciliation immediately, even if it interrupts our schedule of church activities. To God, the anger that we have in our heart is more important than any outward show of religious practices that we might be able to maintain.
Christians will hurt each other, we will get offended and cause offense - that is guaranteed due to the remaining sin in our lives. However churches should be full of people who are seeking reconciliation when those things happen. Instead, churches are too often full of people holding onto grudges against their brothers and sisters or being more willing to stop attending church than attempt reconciliation. We, enemies of God, have been reconciled to God through Jesus' death on the cross, should be seeking reconciliation with others. We, who have been shown mercy, should be showing mercy to others.
Jesus says our righteousness must exceed that of the scribes and Pharisees. They were pleased that they didn't murder. We can not be satisfied that we managed to not hit/slap/bite/shout but we should repent for the anger/contempt/passive aggressiveness that is in our heart and cry out to God for mercy.