In this passage, Paul explains how he uses the right that he has to be payed for preaching the gospel. He begins by asking questions to imply that he is free, that he is an apostle, that he has seen Jesus, and that the Corinthians are his work in the Lord. Then, he says that the Corinthians are the people that show that he is an apostle the most.
In verse 3, Paul begins to defend himself against complaints about a report that he is being cared for because he is an apostle. He begins by implying, with a question, that he has a right to eat and drink. Furthermore, he has a right to have a wife.
Then, Paul uses the illustration of the soldier — the soldier does not serve at his own expense. In addition, he who plants a vineyard eats the fruit of his vineyard, and he who tends a flock drinks the milk of the flock. Moreover, he uses Scripture to prove that those who preach the gospel have the right to gain wages from doing so: the Law of Moses says that the ox is to eat while it is threshing because “the plowman” (the ox) should share in the crops to which he tends. Therefore, in verse 11, Paul implies that it is not too much for him to gain materially from the church, since he has helped it spiritually. However, he says, he did not use that right among the Corinthians because he endures work. He does this to cause no hindrance to the good news of Christ.
In verse 13, Paul uses the example of the Jewish priests, who eat the food of the temple, and from the altar. Likewise, he says, the Lord has given those who preach the gospel the right to be supported because of their job.