In Matthew 5:21-26, Jesus emphasizes the importance of internal righteousness over mere adherence to the letter of the law, illustrating that anger is a form of murder and affects our relationship with God and others. He asserts that harboring anger and using derogatory language towards others are serious offenses, equating them to murder and emphasizing the need for reconciliation before worship. Ultimately, Jesus teaches that true worship is linked to our relationships and highlights our inability to meet God's standard of righteousness on our own.