Summary: There are many misunderstandings about Paul's words on marriage and divorce. Looking at them in the context of the situation they were written in, and context of our purpose as redeemed humans offers us some real wisdom.
Beginning in chapter 7, Paul begins to address specific questions the Corinthians had sent him regarding marriage, eating meat sacrificed to idols, worship, the Lord's supper and the resurrection. First he addresses a question about marriage. If you look at the chapter as a whole the context might be this: "in light of the sin in the world around us, shouldn't we take drastic steps to be more holy?" Those steps might include abstinence in marriage, divorce, singleness, or other radical changes in association or position. Overall, Paul's answer is: "stay put, and stay the course."
Before we look at this section I need to set a context, otherwise we tend to explode what we read into universal absolutes, and text without context is a pretext! So what is the context here? There are three factors: 1) Incredible societal change 2) immense persecution and 3) cultural influence. Before Christianity, women in Roman society were treated as mere property—a little better than children but not much. But in Christ things were different. Paul himself wrote in Galatians 3:28 (quickview)  that there was no longer a distinction between men and women in the body of Christ. This fundamental shift in thinking brought about a seismic wave of change—and there are places in many of the letters of the New Testament meant to keep that change from overwhelming the focus on the gospel. Women who were married to non-Christian men suddenly felt like they could or ought to divorce their husbands to fully embrace the new freedom or so they could be more holy.
The second major context is what Paul refers to in verse 26 as "the present distress." The NET Bible calls it an "impending crisis". We don't know exactly what the persecution was but it was big enough for Paul to adjust his advice about marriage and singleness.
The third is the larger context of the Corinthian culture. So, we come to Paul's discussion of marriage where he answers three questions: isn't it better to abstain, even if we are married? Isn't it better to be single than married? And if we're married to pagans, should we divorce them?
1 – 2
Given the overly sexualized Corinthian society, the church may have concluded that if sex is bad then we should stop it, even if we are married. The HCSB adds quotes around the statement to suggest the question to Paul.
The reality check is that God made us for marriage (Genesis 2:18 (quickview)  "It is not good for the man to be alone."). And in marriage, which is a lifelong commitment between a man and a woman, physical intimacy is the norm, and it is good. (Hebrews 13:4 (quickview)  Marriage is honorable among all, and the bed undefiled NKJV).
Given 1) the power of the need for physical intimacy and 2) the power of the society pulling them and us towards sexual immorality, Paul says we should be married and we should express that union in physical intimacy.
The Corinthians somehow thought that being celibate in marriage would help, but in the end it would only lead to one or the other partner finding intimacy outside of marriage—never ever a good thing.