And did you keep reading 1 Cor. 7?
To the rest I say (I, not the Lord) that if any brother has a wife who is an unbeliever, and she consents to live with him, he should not divorce her. If any woman has a husband who is an unbeliever, and he consents to live with her, she should not divorce him. For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy. (12-14)
So far, so good. People who are married ought to stay married, as a general principle. It's not 100% clear what Paul means in verse 14, but I think we can assume he's answering some question that was raised about what happens to the spouse and children in a mixed marriage. Having an unbeliever in the family doesn't defile the whole family On the contrary, as he says in verse 16, a believing wife might be the instrument of her husband's salvation. So stayng together is better. We can all agree to that.
But then...
But if the unbelieving partner separates, let it be so. In such cases the brother or sister is not enslaved. God has called you to peace. (15)
Paul is always telling Christians to be peaceful: obey the government, don't raise strife with the neighbours, and so forth.This is another example of that. If the pagan husband can't stand being married to a Christian and leaves, don't put up a fight. Pursue peacefulness, and let him go. The Christian wife is no longer "enslaved" (i.e. bound to the marriage.)
I have a friend to whom this happened. She is a convert from Sikhism, and when she became a Christian, her husband deserted her. She wavered for some time one what to do when he said he wanted a divorce, until our then-senior pastor (who is very conservative on divorce) advised her just to sign the papers and let him go. A textbook 1 Cor. 7:15 example.
In other words, there are times when divorce is permissible, possibly even necessary. And once those divorces occur, the marriage no longer exists. Someone who is no longer bound to a spouse is, by definition, free to marry. Otherwise, that would seem like being bound, wouldn't it? If a particular divorce is lawful, so is the subsequent remarriage.
Perhaps it's
better for a divorcee not to remarry afterward. And that is, in fact, more or less where I stand. But I can't say that remarriage would be
sinful in every instance, either.