2. What are Haimon's arguments that he presents to tell Creon he's making a mistake about his judgment of Antigone?

To show that Creon was not right about his judgment of Antigone, Haimon told the story of a captain who was wrong even when he was doing the right thing.

Explanation:

Haimon did not agree with Creon's judgment on Antigone, although Creon was sure he was correct. For this reason Haimon cited a story as a wise and delicate argument to get Creon to reflect on his actions and thoughts about Antigone.

Haimon quoted the story about a captain who left the sails and stretched, because he knew this was the right thing to do and was sure he was doing good to his ship and his crew. However, the ship was tipped over by the wind and the sea, showing that the captain's certainty about the sails was incorrect in preventing the ship from tipping over. With that, Haimon is telling Creon that everyone can make mistakes inside things he believes are correct, so he should reassess the judgment that Antigone was receiving.