In Antigone, how does Creon react to Haemon's arguments?

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When Haemon confronts his father he makes a very sensitive appeal to his better judgement, not openly criticising him but presenting his concerns gently and clearly. He offers many metaphors to support his case, calling for his father to be lenient:

You've seen trees by a raging winter torrent,

how many sway with the flood and salvage every twig,

but not the stubborn--they're ripped out, roots and all.

Bend or break.

However, in response to the voice of reason and moderation, Creon shows himself to be just as stubborn as ever. In a dialogue with his son he protests that the people do not tell him to rule. In a series of revealing questions, he makes clear his position and his belief in his own despotism:

Am I to rule this land for others--or myself?

When he is not able to convince his son of his right to rule the way that he wants to, Creon states that Haemon is on the side of Antigone, calling him a "woman's slave." Being goaded into anger, Creon threatens to kill Antigone straight away in front of Haemon, who in turn rushes out saying that his father will never see him again because of his anger and insanity.