Here we run into a very potent example of the continuity between the Old and New Covenants. Granted, what Paul talks about in this chapter is disturbingly not a sin in to western minds. But even among Gentiles of his day, Paul knew that this issue crossed boundaries well established even outside the Law of Moses.
In the background of our awareness, we know that Leviticus 18:8 prohibits a man cohabiting with his stepmother (or any other woman in his father’s harem). When God made that command at Mount Sinai, it was already a major taboo among most pagan nations, as well. It was considered utterly repulsive for a father and son to have sex with the same woman, regardless of the context. At the least, this was a grave insult to the father. Even the filthy Canaanites would do something like that only as a sacred pagan ritual, not as routine domestic behavior.
It was scandal enough to do this even in Corinth, the capital of self-indulgent hedonism in the Roman Empire. But the offending couple were members of the church! Somehow, at least a portion of church leadership were standing up to defend this, as if it were something God favored, when it was patently obvious He forbade it.
This was such a flagrant breach, such a horrifying defilement of the Body of Christ, that Paul was compelled to demand strong sanctions. This fellow and his woman must be ostracized at a minimum. Then again, that was the most extreme punishment a church body could lawfully exercise under Roman authority. Paul was firm on this; it didn’t matter if he was there in person to conduct any ceremonies. He was there in spirit, and they must agree as one body that this grave sin cannot be ignored.
Paul refers to turning their flesh over to Satan. There are whole books on the implications of this. The point is that God has appointed someone to be His Left Hand to enslave/imprison anyone who walks by the flesh. Satan can’t touch your spirit. Paul emphasizes the point that the flesh must die so that the spirit can be redeemed and rescued from this awful defilement. As long as the man still wants this woman in his bed, he is walking by the flesh, and not following Christ at all. As long as she is willing to be with this man, she cannot claim Jesus as her Savior. If their spirits were reborn, they would be repulsed by the whole idea.
Think about it: Christ Himself would denounce the two of them. He will offer no covering for such people who serve the flesh.
Then Paul refers to the church using this “acceptance” as some kind of public boast to the outsiders. Christ calls us to take up our cross, not to drag every sin we can imagine into His Presence. Referring to the symbolism of leaven, Paul warns that this kind of sin can destroy the church. We need to celebrate the Sparing (AKA Passover) again by cleaning our lives so the Lamb of God can be present.
On the other hand, it’s not as if we could avoid sinners outside the church. Paul had written to them to disassociate from church members who couldn’t be bothered to admit the sexual sins were sin, but that didn’t mean to avoid sinners who didn’t claim to be Christians. The whole point is that sinners are not family. Family might sin, and there was plenty of teaching about how to handle that, but the point here is to discern whether someone was spiritual family or not.