Before digging into the text, I explored its context a little. This letter itself seems to be divided into two sections:

1. [CHAPTERS 1-6]: Issues Paul learned about from people in Chloe’s household (See 1:11: “For I have been informed concerning you, my brethren, by Chloe’s people, that there are quarrels among you,”)
2. [CHAPTERS 7-16]: Issues the church wrote to him about, starting with our current section:
   

1COR 7:1a - "Now concerning the things about which you wrote…"

Paul just finished discussing marital unfaithfulness (the man who had his father’s wife) and lawsuits (the church settling matters in a secular court). So in 7:1 he continues by saying, in essence, “You wrote to me about marital unfaithfulness. Chloe’s people filled me in on what that man did. Now that I’ve instructed you on how to handle that situation, let’s talk more about marriage.”

1COR 7:1b - "...it is good for a man not to touch a woman. "

Literally this says “it is good for a man not to set a woman on fire!” The Greek word which the NASB here translates as “touch,” and which the NIV translates as “marry,” literally means to kindle a fire (see how it is translated in Acts 28:2). But it also means to “touch” passionately. It is the word used in every case when someone touched Jesus or He touched them for healing (such as in Luke 8:46 when He “felt the power go out” from Him), and it’s the same word Jesus used after his resurrection when He told the disciples not to “hold on to” Him (John 20:17). I'm calling this out because we need to be very cautious using this verse to prove that Paul wasn’t in favor of marriage. In reality, he’s taking an even stronger stance than that! His ideal is that a man never even touches a woman passionately, let alone marries her. Celibacy is a beautiful thing. Celibate singleness is best. That’s his message.

1COR 7:2 - "But because of immoralities, each man is to have his own wife, and each woman is to have her own husband."

Realistically, though, few people can resist sexual temptation for a lifetime. So men and women should marry so that they will not become immoral. Later in v. 7 he'll say he wished all men were as he was (i.e., celibate). Even later he’ll say “I think in view of the present distress that it is good for a man to remain as he is” (vv. 26).

1COR 7:3-4 - "The husband must fulfill his duty to his wife, and likewise also the wife to her husband. The wife does not have authority over her own body, but the husband does; and likewise also the husband does not have authority over his own body, but the wife does."

Both husbands and wives live in bodies that belong to their spouses. Because of that, they have a duty to each other regarding sexuality. Anytime someone has something of yours, they owe it back to you. The wife’s body belongs to the husband and the husband’s body belongs to the wife, so they owe their bodies to each other. After all, they are “one flesh” (Gen 2:24, which he just restated in 6:16).

1COR 7:5-6 - "Stop depriving one another, except by agreement for a time, so that you may devote yourselves to prayer, and come together again so that Satan will not tempt you because of your lack of self-control. But this I say by way of concession, not of command."

It’s OK to fast from sex for a time. But notice the conditions for this fast. It must be (1) For a time rather than forever, (2) By mutual consent, not by one partner’s frigidity, and (3) So that you may devote yourselves to prayer, not so you can punish each other or grow further apart. These limitations on sexual fasting are provide to avoid Satan’s temptation and “because of your lack of self-control.” He’s not commanding them to fast from sex (v.6). He’s simply giving them the option if it’s for the purpose he described.

1COR 7:7 - "Yet I wish that all men were even as I myself am. However, each man has his own gift from God, one in this manner, and another in that."

The ability to remain pure in celibacy is a gift from God. Not everyone is gifted in that way. Those who are should stay single. The rest should marry.