The point in 1 Corinthians 9 is that Paul is no longer under the law but being in Christ has become free unto the law of Christ. The gospel, the good news, is that we are free from the that says my right my want to consider others as more important than ourselves.
The whole context of 1 Corinthians is that of combating issues of disunity within the church. Essentially Paul deals with the quite essential reasons why there are disunity or breaking of fellowship. His last reason and most compelling and important one at that is that their doctrine of the Gospel was messed up. Without a great foundation a house will not stand together not only congruently but perhaps maybe even permanently as foundations shifts and moves the house will suddenly break apart and tumble down eventually. The issue of the church was not their view of the law, but of much extreme importance of the gospel - the resurrection. If Christ has not been raised, then we are still caught in our sins and are most to be pitied never mind the thought that we will then be shown to be most morally good and perhaps praised. Paul knocks this thought down right away in Chapter 15 verse 18.
So with that the law cannot bring unity but only disunity. As Albert Mohler Jr (President of Southern Seminary) says in his book Culture Shift, The city of man is disunified, whereas in the city of God the ruler is God and all are unified under His rulership. Those who are outside of Christ are under the curse of the law and its demands and burdens. No one is free there is no unity to be had in the works of the law. Some might charge this Antinomian - I don't see it this way. The law is preached to those who are dead in trespasses and sins to show them that they have not obeyed and are not righteous but have fallen short of God's glory and are under His just wrath and anger. Paul says in Romans 8 however that God has done what the law weakened by the flesh could not do and that is essentially break down the curse and save humans from the corrupting power and decay of its power by work of the Spirit. In Christ God has not only punished sin but He has justified sinners (Romans 3). Therefore Paul could explain that there is Therefore NOW no Condemnation for God's elect (those who are IN CHRIST). Finally it has been done. The debt has been Paid, nothing do I owe.
So going back to the ninth chapter of 1 Corinthians Paul says that he most certainly does have a right to eat and drink according to his privilege as an apostle, however, he does not take up his privileges but rather has surrendered his rights (v. 12; v. 15). The reason why he has surrendered his rights and could do such is because he is not under the law. Paul in verse 19 - 23 says that in order to win some not under the law he becomes like one not under the law and to win those who are under the law he becomes like one who is under the law So that He might win some to Christ. He could do this because he is not under the law but is in Christ who has become for him a new 'law' - that is the law of love in which believers who are in Christ stand in unity of because of the Gospel truth that Christ has died and has been resurrected destroying both sin and death so that by faith repenting of their sins and trusting in Him alone they might also live freely unto glory.
So with that Paul is able to say that "But I discipline my body and
keep it under control, lest after preaching to others
I myself should be
disqualified." He can only do such by surrendering his rights and can only surrender his rights only in Christ.