For the church to grow spiritually and be blessed by God, any and all sin must be put away. When a congregation becomes aware that sin is among them they must act to rid the “body of Christ” of that sin. If they don't the presence of God and Jesus will not enter that group. So, Paul writes 1Corinthians (as a whole) to test this church to see if they would be obedient in everything, but he inserts a very troubling situation “a type of sexual immorality that even the pagans reject” and requires the church to expel this individual. Paul uses these stern words: “deliver such a one unto Satan for the destruction of the flesh”(1Cor. 5:5) not in a vindictive way, but in a way of hope! The idea of being turned over to Satan is quite frighting and Paul's use of words worked! This man repented and was looking for forgiveness, but he wasn't getting it. This example is where this church failed and Paul needed to remind them that when a sinner truly repents, they should welcome the individual back into the church and show “love” to him (1Cor. 13). Paul addresses this in 2Cor. 2:5-11.
Update: When we read the words in a book and consider them truth we can easily be deceived (myself included). This has occurred with this question and the statement: "a type of sexual immorality that even the pagans reject." The facts recorded in history actually state that the Greeks and Romans had extremely liberal sexual practices. The ancient Greek and Roman sexual laws mostly related to marriage. When Gentile marital laws were broken, the offending female spouse could be killed, but men were not severely punished. Jacob's firstborn son Reuben was cursed because he had sex with his father's concubine (wife) Genesis 35:22 and 49:4. The related story does not state that the offender married his father's wife or even if his father was still alive. It was common knowledge that if a husband died, the wife was released from the marriage laws (this law caused many to be killed because of the beauty of a woman; example: King David). This could also explain why the Corinth church didn't think this was a big deal. We also have to consider whether this woman was actually his father's concubine, which again would be considered a different category by Gentiles. So, with this new information, I now take the position that the statement in question is probably “spurious” and was added by a second or third century copyist. This is about the time when stricter sexual laws were implemented. [but in many cases not obeyed (somewhat like today)]. These statements do not alter my support for all of God's sexual laws and it seems that Paul supported them as well.