Why does Paul ask what advantage does the Jew have?
He isn't himself asking if the Jews have an advantage. Rather, he is asking the question that is probably on everyone's minds.
Paul just explained in the last chapter that both Jews and Gentiles are the same, because even though the Jews have the law, what matters is a new life and a new heart that truly loves God. Naturally, the readers of the letter would ask "if the Jews and the Gentiles are the same, then what advantage does the Jew have?"
What does the phrase mean "Let God be true though everyone a liar"?
God's truthfulness and faithfulness doesn't depend on other people. He is in Himself true.
"We are to believe God's truth if nobody else believes it. The general consensus of opinion is nothing to a Christian. He believes God's word, and he thinks more of that than of the universal opinion of men." -Spurgeon
The opinions of your peers about God should not be the ultimate source of truth in your life.
Why shouldn't we rely on the opinions of our peers when determining truth about God?
They are not accurate. They are by nature against God. They will reason against God.
What claim is Paul arguing against in this section?
He's arguing against the claim that if doing bad results in God showing His truth and righteousness, why not do bad things?
"why not do evil that good may come?"
What is Paul's answer to this claim?
We all know that God will judge the world. How can He do that if we were to agree with the claim. If we agree with the claim, then God should not punish us because good came out of it.
"If God somehow accepts the unrighteousness that is an occasion for His mercy, should He not welcome even more acts of unrighteousness from us? This conclusion is foolish...The end does not justify the means."
What is the purpose of this claim?
People who make this claim are using this claim as an excuse to sin and do whatever they like.
What are some thoughts that go through our heads when we are trying to justify sin?
What does it mean to be "under sin"?
"doesn't seek for God"
"their throat is an open grave...their mouth is full of curses"
"their feet is swift to shed blood"
"there is no fear of God"
Why does Paul conclude what he concludes in v20?
Paul concludes that since no one is righteous, no one can be justified in God's eyes through works of the law.
justified (adj): having right standing with God
Why does it matter if I am "under sin" or not?
Because if you are under sin, you will not have a right standing with God. and not having a right standing with God prevents you from being in fellowship with Him. Have you ever felt empty inside? Have you ever wondered if there's more to life than just this?