To start with, I believe from my study that the theme of 1 Corinthians is spiritual maturity. Everything Paul deals with is heading toward encouraging Christians to be completely mature in their faith.
In chapter 8, Paul is answering the question from the Corinthians which was addressed to him in a letter about whether it was right to eat meat which had been sacrificed to idols. He begins his discussion of this subject by saying that knowledge can make a person proud and arrogant, but love will build up the other person and seek their best. This will be important in his discussion. He then goes on to make it clear that an idol is absolutely powerless and worthless, therefore to have anything sacrificed to one of these inanimate objects means nothing. He continues the discussion, however, by saying that there are some Christian brothers and sisters whose faith is not strong and they are unable to eat this meat without it defiling their conscience. I believe Paul is saying with this line of argumentation that these people are immature in their faith. He continues, though, by giving the mature view of Christian liberty – that the mature Christian will set aside his freedom to indulge in that meat for the sake of the weaker (immature) brother. That is the short view of chapter 8.
Chapter 9 is an illustration from Paul’s own life of how he uses his Christian liberty. He starts off with a series of rhetorical questions that show his apostleship and the right he has to expect certain rewards and treatment because of that apostleship. His overall point is that he has the right to have a wife and travel with his family and expect the churches to take care of him and his family financially. Then he begins his example of how he sets aside this liberty he has to expect this treatment. He willingly preaches the gospel and asks for nothing in return, because he does not want anyone to ever get the impression that what he does is for money. He then closes his illustration from his life by making the statement that he would become “all things to all people” in order to present the gospel to them. My interpretation of this is that his use of Christian liberty is not to bring himself pleasure, but to be flexible enough to participate in whatever the activity that did not cross the line into sin. I say this because one of the statements he makes is that he will become a Jew to the Jew and a Gentile to the Gentile in order to see them come to Christ. The way I see this is that when he was with Jewish people, he willingly at Kosher, although he realized that God did not require this of him. When he ate with Gentiles and they served pork, he would utilize his freedom in the opposite direction and eat the pork. Everything he did was for the purpose of forming relationships that would lead to salvation of the individual.
For now, that is all that I am going to discuss, but stay tune to part 2 covering chapter 10.