Actually, Paul DOES think that celibacy is possible and he only recommends marriage as a second best alternative for those who "burn" with lust. Note as a basic historical fact that Paul was celibate himself, as were many other early Christians and members of other ascetic groups such as Pythagoreans. Also, Paul was a strong advocate of celibacy within marriage when possible.

21st century popular culture notions of sexuality should not be read back into the Bible or attributed to St. Paul.

What Paul is saying here is that it would be better if people did not have sex, but that is not really realistic.  Because it is not, people will have sex, but they should be sure to do it within marriage.

In the previous verse, Paul is citing something the Corinthians have asked him.  They have asked whether it is better not to have sex.  He agrees that it is, but that that is impossible.  Therefore, he goes on to say, people should give themselves freely to their spouses within marriage.  The desire for sex is strong and should be indulged.  He goes on to say (read all of verses 1-7 to understand) that wives and husbands must willingly have sex with one another.  The implication (strongly given in verse 2) is that they should only have sex with one another.

So, Paul is saying that sex within marriage is acceptable because it is not realistic to be celibate.