For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. Romans 1:16
Back in my Bible College days, I memorized these verses as an aid to my newly-acquired soul-winning endeavors. At first, I dreaded approaching strangers with "God's plan of salvation". Even more so, people I knew. Believe me, I needed the encouragement to "keep on keeping on", and I slowly did get more accustomed to witnessing. Every so often, I wondered if the supposed shame I struggled against might not be more closely related to the overwhelming panic I experienced at any kind of public speaking, even one-on-one confrontations like asking the boss for a raise. After all, Paul did not suggest that his lack of shame related to the fear of approaching people with a message, but rather with the message itself. I also had to consider the fact that his statement did not specifically refer to preaching to unbelievers, for this message was directed to the believers in Rome. That didn't make much sense to me, but I've come to realize that we pretty much ignore what doesn't make sense.
So then, what other possible shame could Paul have referred to? What does the gospel declare that might give a believer cause to feel shame? And no, it is not sin.
For consider your calling, brethren, that there were not many wise according to the flesh, not many mighty, not many noble; but God has chosen the foolish things of the world to shame the wise, and God has chosen the weak things of the world to shame the things which are strong, and the base things of the world and the despised God has chosen, the things that are not, so that He may nullify the things that are, so that no man may boast before God. 1 Corinthians 1:26-29
You see, believers don't often come from the ranks of the world's wise, mighty or noble, but from that which is rated as foolish, weak, base ... even from among those who are considered the nothings of the world. But where there is cause for shame in the world, God has removed it in Christ.
But by His doing you are in Christ Jesus, who became to us wisdom from God, and righteousness and sanctification, and redemption 1 Corinthians 1:30
Ironically, I have come to realize that I actually dreaded public speaking for the same reason I might find shame in the gospel: exposure as being deficient. After all, why would it surprise me that the salvation of the gospel impacts the exact same basis of fear that paralyzed me in the world? Of course in the world, I have the ability to improve my temporary standing by playing the game. In other words, I can get better. However, by declaring my real value in Christ, I can only make myself appear more deficient to the judges of this world. All things considered, I am not ashamed of the gospel.