I understand that presumption of your second sentence and how that applies to many of the "sexual immorality" verses people will choose. That is specifically why I choose the verses I did, because that presumption does not have to be there.
Go back to the logic:
Paul said if you burn with passion you should marry. However, if pre-marital sex were OK, then the solution (in fact the simplest, quickest solution) to burning with passion would include pre-marital sex. But it does not. The choices are clear and there are two. Deal with it or get married.
"Deal with it?" Very well, I shall. Let me follow Paul's argument line by line, starting from 1Cor 6:12.
12: You claim it's alright to do anything you want, but the problem is that not everything is good for you.
13: You say, "we have a stomach for a reason." True, but the body is not made for (word of the day), but instead for the Lord.
If the word of the day means unsanctioned sex, why set it in antithesis against "The Lord?" Why not say "but instead, the body is meant for marriage?" Rather, Paul said "the body isn't made for immorality, the body is made for the Lord." Paul was talking about giving the body to a temple prostitute, which is why he goes on to talk about uniting Christ with a prostitute. "The body isn't meant for (fill in the god), but instead for the Lord."
14: God raised the Christ with His power, and He will do the same to us.
15: Your bodies are part of Christ's body. Don't unite them with a prostitute.
16: Sex is union. Unite with the Lord, not a prostitute.
If Paul is talking about anything other than a temple prostitute, he makes a very strange message. "Don't be one with a prostitute, be one with the Lord." Why contrast two dissimilar things? He even makes this clearer when he adds on about being one with the Lord in spirit. The union being avoided was a spiritual one (temple prostitutes), therefore the logical answer is a spiritual one. Otherwise, why wouldn't he go ahead and jump into his message of each man having his own wife? Married men still went to temple prostitutes, that's why.
18: Flee from "sexual immorality." This sin affects your body.
What body? The body mentioned in v15, Christ's body. The focus is spiritual, and the spiritual union that comes from the temple prostitutes.
19, 20: Your bodies are temples. Honor God with them.
Chapter 7, 1-5: You say it's good to not have sex, but because there is so much of ^this going on, you should each have your own wives (or husbands) and have intercourse with her(/him). Don't withhold each other's bodies, because you belong to each other.
So Paul is definitely talking about temple prostitutes and not pre-marital sex. He says absolutely nothing (here) about
getting married; he is talking to people who are
already married. Verse 5 nails...er, uh,
clarifies what he means: "Don't deprive each other." People were withholding sex from their spouses, which is why he has to command them not to do so.
Finally, in verse 8, Paul begins to talk about unmarried people. What should they do? Get married if they want to; and yes (again) that's the best option. See Genesis. But Paul says nothing after suggesting marriage about sin, atonement, Christ, the power of God, or any of that. There is no mentioning about "sinning against his own body."
Sexual relationships are clearly intended for marriage (or possibly vice-versa). But there is never any mention of pre-marital sex being sinful. "If you can't control yourself, then dude, go ahead and get married" is a far cry from what everyone is trying to say.