When Paul says to cast the man out of the church who is sleeping with his father’s wife, it is important to remember everything that he says, lest we miss his point. He begins in verse four with:
Let him who has done this be removed from among you.
But that is not all. A couple verses later he adds:
When you are assembled in the name of the Lord Jesus and my spirit is present, with the power of our Lord Jesus, you are to deliver this man to Satan for the destruction of the flesh, so that his spirit may be saved in the day of the Lord.
This is not punishment for no purpose. Paul instructs the church in a way to enact discipline on this man for two reasons. What we see in the verse quoted above is “so that his spirit may be saved.” It is the difference between a strictly punitive action and a restorative one. Paul wants the church to, by their expulsion of him, restore his soul. If he wants to be part of the body again, he’ll have to turn from this sin. He can’t just go to the more open-minded church around the block in Corinth. This is his fellowship to which he would seek to restored.
The other purpose in casting out this man, a man who has sinned in such a way that even the extremely permissive Roman society would condemn him, is to guard the body of believers. His sin is not harmless. It is like a leaven that makes it way into the whole dough. Paul wants to protect this people who he cares greatly about. He’s already compared himself to a mother and a father in his relationship to them. He knows that if this influence remains it will affect the whole church.
So rather than recommend what may have been a Jewish judgment of incest, stoning, or delivering this man before Roman courts for the Roman law he has broken, Paul instructs the body to do something that may save the man’s spirit on the day of the Lord and will protect the life and witness of the church in Corinth.