In verses 21 to 48 Jesus provides a fuller explanation of the OT law in six examples. They illustrate a righteousness that goes beyond the outward correctness of the Pharisees and scribes.
Anger.
v.21-22 Here Jesus quotes the OT prohibition on murder from Ex 20:13. Murderers were subject to judgment (Nm 35:31). But Jesus teaches that everyone who is angry with his brother (without cause) is also subject to judgment. In this context, “brother” means anyone among Christ’s disciples. The basis is that each person is made in God’s image and we need to value our brother (or sister in Christ) as God values him. It is not only outward murder, but also inward anger (that could lead to murder) that violates God’s prohibition on murder in the Ten Commandments. Where unjustified, Jesus also condemns the use of insulting names.
v.23-24 Reconciliation with a brother should take priority over even offering a gift in worship. This is not one’s own anger but the anger of a brother that needs to be dealt with. Anger between you and a brother can effect your relationship with God and should be dealt with immediately.
v.25-26 To not get reconciliation can have disastrous effects as shown in the example in these verses. Here we are dealing with an adversary who apparently has a monetary claim against you. Settle with him out of court or you may go to prison until you have paid the last penny.