Why did Paul use the vineyard and flock examples in 1 Corinthians 9?
Paul used the vineyard and flock examples to demonstrate that a worker deserves compensation: a vineyard owner deserves a return for labor and capital, and one tending a flock partakes of its milk. As an apostle, he had that right, yet he refused support so no one could accuse him of serving for money.
Les teaches that Paul brings up the vineyard and flock to show that as an apostle he deserved a certain compensation for his time, his suffering, and all that. A vineyard owner deserves a return for his labor and capital, and someone caring for a flock of goats, sheep, or cattle should partake of the milk they produce. But Paul never took that pay. He did not want anyone to point a finger at him and say he was just doing it for the money. Les suggests another reason: Paul had seen in Judaism how money could corrupt him, and Les points to Galatians chapter 1 while relating this to his own fear that taking money can make a person greedy.