If Athens was known for its idolatry, Corinth was consumed with immorality. Paul’s preaching and reasoning in the synagogues led to his being opposed and reviled by the Jews.
He responded by shaking our his garments and saying to them, "Your blood be on your own heads! I am innocent. From now on I will go to the Gentiles."
Paul knew that lives were at stake; he was blood-earnest in the way he spoke. And people were saved as a result.