In order to illustrate to the Corinthians how they should be more concerned about others than themselves, Paul used himself as an example. He showed them that though he had a right as an apostle and a preacher to be supported by them, he did not exercise that right because he didn’t want to do anything to cloud his message.
This is not to say that preachers and missionaries who take remuneration for their work are wrong, but it is simply an example of how careful Paul was to limit his right for the sake of the gospel.
He goes on in the chapter to show that he was very sensitive to the preferences of the groups he was around, and, as much as he could without compromising the gospel, he adapted.
These were not the decisions of an unstable man. On the contrary, they were carefully made so as to see more people saved, to please the Lord, and to win the prize of God’s rewards.
How much are we focused on defining and defending our rights and privileges? How much are we concerned about giving up our rights for the sake of the gospel? May God help us to do more limiting of our rights for the gospel’s sake.