One of the most central conflicts in Antigone is character vs. society, or character vs. state. Antigone is finding herself at odds with society, or the state, because the new King Creon has issued an ordinance that she finds morally objectionable. In addition one of the most central themes in Antigone concerns the idea that both stubbornness and tyranny lead to destruction. Antigone's conflict with Creon enhances this theme in a couple of different ways.
One way in which the conflict enhances the theme concerning stubbornness and tyranny is that it portrays Creon as clearly both stubborn and tyrannical. He acts stubbornly by refusing to consider Antigone's emotional need to bury a loved one and by refusing to listen to anyone's council but his own, including the all-wise and all-knowing soothsayer Tiresias. He acts as a tyrant by considering himself to be the ultimate authority. When Haemon begs his father to release Antigone, telling him how disturbed the city is by Creon's punishment, Creon's response is to say that he refuses to be ruled by his city, and furthermore, that the city belongs to the ruler, rather than the ruler belonging to the city, as we see in his line, "The city will tell me how I ought to rule it?," followed by, "Isn't the city thought to be her ruler's?" (745, 749). Hence we see that because Creon represents the state, or even the regulations of society, Antigone's conflict with Creon helps to portray his character as stubborn and tyrannical and to elude to the dangers of both these qualities that the theme speaks of.
Another way in which Antigone's conflict with Creon serves to enhance the theme is that it serves to characterize Antigone as stubborn and headstrong as well, which is portrayed as equally dangerous as Creon's tyrannical nature. While defying unjust laws and even dying for what you believe in can be seen as laudable, time and time again Antigone is referred to as foolish in the play, especially by the chorus. The chorus points out that Antigone is as headstrong as her father and does not know when to yield to authority, as we see in their lines, "She is clearly the fierce daughter of a fierce father; she doesn't know to bend with the wind" (485-486). In addition, while the chorus tells her that her choice for early death will make her famous, they also tell her that she was too bold and went too far in defying the law:
You went forward far too boldly
and crashed into the lofty
pedestal of justice. (859-861)
Even Tiresias argues later that stubbornness is foolish, as we see in his line, "Obstinacy brings the charge of stupidity" (1031-32). Hence we also see that Antigone's conflict with Creon also serves to illustrate the theme concerning stubbornness, showing us that stubbornness is just as dangerous and foolish as tyranny.