In chapter seven Paul is continuing his discussion of sin in the church body, and specifically sexual sin. He isn’t making a simply moralistic argument about what is proper for a Christian community rather it is a theological argument.
Paul doesn’t base the conduct of the church on any passing norms in the culture. For the sake of argument he even acknowledges the church in Corinth’s thought that all things are now lawful for us in Christ. But Paul says that just because something is permissible, that does not mean it is good for the body. Our bodies have a purpose and it is not to satisfy sexual desire. We are not our own, rather we are Christ’s. And we serve his purposes.
Memorizing 1 Corinthians 6:19–20 will serve us well in remembering what we are called to do with the bodies God has blessed us with.