Paul argues against an objection to salvation he has probably heard. If our sin causes God to become more righteous by forgiving more sin, is our sin a good thing? Paul outright condemns that kind of thinking. Obviously God is not in favor of sin! He then paints a very negative picture of humanity with various quotes from the Old Testament. Every person who has ever lived is a terrible sinner! God’s righteousness is demonstrated in that he makes righteousness available to everyone through the death of his son. All anyone needs to do is believe.
If you are trying to earn your way to righteousness, you are making the situation worse. You are acknowledging that God has the right to judge you, but hope he overlooks the ways you fall short. The right answer is to realize your sin and depend on God to forgive you through Jesus’ death on the cross.