Chapter nine continues the teaching on Christian freedom, expanding out from the initial question about food dedicated to idols. In order to expound on that more, Paul demonstrated how he treated others. There should have been no question as to whether or not Paul was an apostle, which meant he should have full access to the freedoms we have in Christ (1 Corinthians 9:1-3).
When he was asked about how to live out his freedoms, he pointed to his ministry (1 Corinthians 9:4-12a). As an apostle, he had the right to have a wife and minister alongside her. As an apostle, he had the right to be financially supported by the people he had pointed to Christ and the churches he started. The other apostles did that, and he had those rights as well. In fact, it made no sense that his spiritual children should not take care of his financial needs, and he gave a series of illustrations to prove it.
As he showed in chapter eight, however, the question is not one of rights and freedoms but love. The fact that he had those rights did not mean that he forced them on others. In fact, in many cases he did not exercise his rights, “so that we may not be a hindrance to the gospel of Christ” (1 Corinthians 9:12b-18). Paul chose to forego his rights and freedoms, because he had been charged (and may have been accused even in Corinth) of being like the traveling charlatans, snake-oil salesmen, who deceitfully sold their wares then left town. Because of his itinerant ministry, Paul chose to not take funds from the places he was preaching, so that when he left town, the new believers would not feel taken advantage of, thereby hurting the gospel ministry.
Broadly speaking, then, Paul chose to use his freedoms to make the most of the opportunities, depending on whom he was ministering to (1 Corinthians 9:19-23). Rather than flaunting his freedoms, he chose to limit them for the benefit of those around him. This is what he meant when he wrote several years earlier, “For you were called to freedom, brothers and sisters; only do not use freedom as an opportunity to indulge your flesh, but through love serve one another” (Galatians 5:13).
Ultimately, he refused to let his personal desires control him (1 Corinthians 9:24-27). Doing so could disqualify him from future ministry. Instead, he controlled his desires. Even though it was uncomfortable or restrictive sometimes, it was better that people came to know Jesus than that Paul maintained his personal freedoms and rights.