Paul said this when expressing his feelings about presenting his gospel/teachings.

Ashamed in today's understanding means "embarrased", and I wondered about that. Why Paul might think that his readers would feel he had any reason to be "embarrased"  to present the truth.

Then I read the meaning in Greek, as presented in the Concordant version of the New Testament. In its glossary it explains that Paul is telling us that he is not "disgraced"..it is no dishonor for him to teach that which is not known by most people, or in other words, he sees not need to worry how others feel about  his gospel.

Why? Because it came straight from the "horses' mouth", so to speak..pardon my crudeness.  He was taught this gospel by the Spirit of God!  

There's no need, therefore, to back away from others who might challenge him.

When he appeared before the original Apostles and James, the brother of Jesus, he didn't back down, "stuck to his guns".  He knew he was right in not demanding that those who followed him need to become Quasi Jews..what they ate made no difference, as long as it wasn't food for idols, and there was no need for circumcision to mark that they were "chosen" people..they were followers of Jesus Christ, and they didn't have to live by the "Law".

Paul realized that this would present a "stumbling  block" to acceptance, and so he cautioned his followers to broach these differences with tact and with careful deliverance, so as to avoid this occurring.

This idea of a "stumbling block" was presented in the Old Testament, indicating that something should not be the cause of acceptance, so Paul, as any good teacher does, used this as a reference, moving fron "the known to the unkown". 

To the pagans, "Greeks", who were use to worshipping many gods, his message was also difficult to accept. They sacrificed humans to their gods, when the signs were not favorable. How could they possibly accept one God, who was  seeking no sacrificie, after all these years. Yet, Paul gave them the same message and some accepted and believed..through the grace of God.

Now, some of you believers, who suddenly have  "seen the light", grasped the truth, may be tempted like my friend John, who use to attend bible study at the BAPTIST CHURCH, and  told them they were wrong in their belief, and wondered why they didn't believe him!

He was reminded that only through God's grace is this possible, but he kept trying.

So,  tread carefully, and be selective in whom you might try to convert from their life-long understanding to that of understanding and accepting Pau'ls truths..paulnbob