Pastor Robbey emphasizes the importance of managing anger while highlighting that anger itself isn't a sin, as long as it's directed correctly. He encourages righteous anger that aligns with God's displeasure towards sin and hypocrisy, contrasting it with unchecked anger that can lead to bitterness and division. The pastor warns that harboring anger opens the door to the devil and can have destructive consequences in our lives. He calls for self-reflection on the nature of our anger and urges individuals to seek reconciliation and divine forgiveness to foster healing and peace.