7:1-16 Paul speaks to those who are already married. 7:17-24 Paul states the overall theme: "Do not seek a change in status." 7:25-38 Paul speaks to those who have yet to be married.
A quote from the Corinthian letter: "It is good for a man not to have relations with a woman" (original Greek word not about marry or not marry). Sexual abstinence is another expression of their "spirituality" with its negative attitude toward the material world and the body.
The phrase "sexual immoralities" (plural) indicates the enormity of the evil or possibly a great number of problems such as adultery, fornication, and prostitution. Solution: "Let each man who is already married continue in relations with his own wife, and each wife likewise."
Sexual relations are a "due" or "duty" within marriage.
The body is not one's free possession but belongs to one's spouse. The emphasis is not on "possessing" the body of the other; rather, an attitude that I do not have authority over my own body, to do with it as I please. (Note the non-complementarity of Biblical principles: a teaching may demand one's own compliance yet it cannot be insisted for similar compliance from others.)
"except"="unless perhaps" (a hypothetical modification, not the norm). Stop "defrauding" (same verb used in 6:7-8). Two conditions: both agree to it, and for a set time.
Even such a good thing as temporary abstinence for prayer will not be raised to the level of command but only as a concession.
Celibacy is a spiritual gift (Greek charisma, gracious gift). "Another has that" may mean that marriage is also a spiritual gift.
"The unmarried" may be translated as "widowers" because the same word in v.34 is used in contrast to the "virgin" (one who was never before married).
"if they cannot control themselves"="if they do not practise continence" (or exercising self-control): the term refers to those who actually practise sexual immoralities.
Here, both partners are believers, in contrast with "the rest" (those with an unbelieving spouse).
Believers are not to initiate divorce. When Paul has no direct command from God, he still speaks as one who is trustworthy (v.25) because he has the Spirit of God (v.40).
If the husband/wife is holy, then the unbelieving spouse and the children are also "holy", that is, set apart in a special way that hopefully will lead to their salvation.
One is simply not under bondage to maintain the marriage if the unbeliever wishes to dissolve it.
"if the unbeliever leaves"=abandonment or desertion of marriage which may be physical, financial (not providing support) or emotional (persistent physical abuse or drunkenness)
Paul prefers that they follow "God's call into the ways of peace," meaning that they should "stay as they are" within the marriage and view that on the one hand as God's calling (v.17) and on the other hand as an opportunity for the salvation of the spouse (v.16).
The conjunction "nevertheless" ties to what precedes: change is not to be the rule. We are not commanded to retain our present social setting (v.21), but that we need to recognize that God called us to salvation while in a certain social setting and that setting becomes the proper one (as if it is "assigned" by Christ) in which to live out life in Christ. In the present context, that means being married (whether to a believer or an unbeliever) or being unmarried.