"But to the married I give instructions, not I, but the Lord... But to the rest I say, not the Lord..." 1 Corinthians 7:10-16
Who or what are "the rest"? Does anybody actually know? If verses 10-11 are addressing the married, then "the rest" would logically mean anyone who is not married, right? But verses 12-16 continue speaking about husbands and wives. So what is meant by "to the rest"?
Paul just forbid divorce for married people in verses 10-11. So who are being addressed in verses 12-16 if not the married? If it is not talking to the married, then you really cannot claim that it is talking about an exception for divorce, can you? You could not do so anyway since verses 10-11 just prohibited it. Since Paul does not have a forked tongue and does not speak out both sides of his mouth, he quite obviously did not prohibit divorce in verses 10-11 and then give an exception in verses 12-16. Since the words in verses 10-11 are a direct command from the Lord Jesus, Paul certainly did not just turn around and willfully contradict His Lord and Saviour.
"The rest" could only refer to single people and widowers/widows, right? But then the rest of the passage is problematic since it goes on to speak of husbands and wives, which single people and widowers/widows do not have. The fact this passage continues speaking about husbands and wives is evidence that "to the rest" cannot possibly mean someone other than the married.
There is no group of people that what was said in verses 10-11 does not apply. If you are married, verses 10-11 apply. Verses 12-16 let us know that if we are married to an unbeliever and they are content to live with us, then we should continue to live with them. They may end up saved through us. If they want to leave, then we should let them leave so that there may be peace. If we try to force them to stay, our lives will be like the problematic spouse we read of in the book of Proverbs. This passage nowhere gives occasion to re-marry. If our spouse later becomes saved and wants to reconcile with us, how will they be able to do so if we are married to someone else?
People can try to rationalize their sin all they want, but God's Word is exceptionally clear. We do not want to accept it or obey it because we are rebellious and hard hearted, just as the Jews were. But the Lord Jesus calls us to a higher standard. We are called to be imitators of Him. If marriage is a picture of the Gospel, which it is, and if it is a picture of Jesus and His Bride, which it is, then do you honestly believe Jesus would allow for something that will deliberately mar that picture? Or would Jesus call us to something hard but extremely beneficial for our sanctification? I think you know the answer.
"To the rest" obviously and clearly cannot be referring to another group different from "to the married" because it continues addressing husbands and wives, who are "the married." "To the rest" more than likely means either as to the other part of your epistle, or as to the cases of the rest mentioned in your epistle. Based on the context of verses 12-16, we may infer that verses 10-11 are speaking to husbands and wives who are both believers. Then verses 12-16 address husbands and wives where one is yet an unbeliever.
In verse 25, Paul says, "Now concerning virgins," and then in verses 27-28 adds, "Are you bond to a wife? Do not seek to be released. Are you released from a wife? Do not seek a wife. But if you marry, you have not sinned. And if a virgin marries, she has not sinned." There are three types of people mentioned in these two verses: the married, the widowers/widows, and the virgins.
How do we know that those who are "released" are widowers/widows? Because Romans 7:2-3 and 1 Corinthians 7:39 are extremely clear.
"For the married woman has been bound by law to her husband while he is living, but if her husband dies, she is released from the law concerning the husband. So then, if while her husband is living she is joined to another man, she shall be called an adulterous. But if her husband dies, she is free from the law, so that she is not an adulteress though she is joined to another man." Romans 7:2-3
"A wife is bound as long as her husband lives; but if her husband has fallen asleep, she is free to be married to whom she wishes, only in the Lord." 1 Corinthians 7:39
People can try to explain these verses away all they want, or try to ignore them, but there is no mistaking what is being said. Romans 7:3 agrees with everything Jesus said in Matthew, Mark, and Luke; namely that re-marriage, except in the case of a dead spouse, constitutes adultery. The only way you are "released from a wife" is if she has died. Scripture provides no other legitimate release from the marriage covenant. Not in Matthew 5:32 or 19:9, and not in 1 Corinthians 7:15. Anyone who tells you any different is lying, whether ignorantly or deliberately; their teaching is in error.
I hate to do a shameful plug, but if you want to read a clear exposition and exegesis of every passage affecting the issue of marriage, divorce, and re-marriage, I encourage you to pick up a copy of my book The Bible on Divorce and Remarriage.