I gather that, this past Sunday, a lot of people heard that the body is not for immortality. (That's not unbearably bad, as the passage goes on to say the body is "for the Lord, and the Lord is for the body; God raised the Lord and will also raise us by His power." If you don't mind your natural end being different than your supernatural end, a case could be made that... ah, never mind.)
The words that popped out at me on listening to them, though, were from verse 19:
Do you not know ... that you are not your own?
And, well, no. I don't know that. At least, I might say that I am not my own, but I certainly live as though I were my own.
But if I am my own, then I cannot be holy, which is to say, I cannot be dedicated to God, which is what St. Paul explains in the words I elided from verse 19: "that your body is a temple of the Holy Spirit within you, Whom you have from God." St. Paul is speaking of sexual immorality, but it's true in general: the Christian is not his own, any more than a building given to God and consecrated as a church belongs to the one who donated the building.
We do know of a case where someone tried to have it both ways, to keep his property while announcing that he was giving it all to God, but that didn't turn out well for him.