Creon is a rather weak man who has been thrust into a position of authority and is afraid he won't be able to handle it. As a result, he doesn't dare reconsider any of his decisions--doing so, he thinks might make him appear weak and cause his subjects to lose respect for him. So when he orders that Polyneices be left unburied and then orders Antigone to be entombed alive when she's caught violating the order, he can't let himself listen to her or Ismene or to Haimon. He even refuses to listen to Teiresias, conveying the displeasure of the gods, until Teiresias has left, but in fact that message offers him a face-saving way out, he thinks that no one can call him weak for backing down in the face of divine displeasure. However, he makes the same mistake Teiresias has accused him of: getting things backwards. Teiresias points out that he has buried the living and left the dead unburied, and now, when the chorus advises him to free Antigone and bury Polyneices, he does those two things in reverse order, so that Antigone is left in the tomb to despair while Polyneices is being given a royal funeral, and she hangs herself. At the end, after her suicide has led to that of Haimon and his to that of his mother, Creon must face the fact that his misguided stubbornness has destroyed his personal world.
Antigone's tragic flaw is her pride and loyalty to the gods and their rituals because she wants to bury her brother so that his spirit will be at rest. She didn't bend to the laws of Creon and buried her dead brother anyway; losing her potential husband \and her life. But then again, she gained the respect of her fellow towns people who admired her bravery and she succeeded in burying her brother under the will of the God's.