Antigone is one of four children of Oedipus, King of Thebes, who blinded himself and went into self-imposed exile with Antigone and her sister Ismene when he found out that he had killed his own father and married his own mother. Oedipus's wife, and also his mother, was Jocasta, who committed suicide, basically for the same reasons. Antigone had a pretty rough start in life.
Things didn't get much better for her. By the time we meet Antigone in Sophocles's Antigone, she's a grown woman, independent and headstrong. Her father, Oedipus, is dead, and her two brothers, Eteocles and Polyneices, have killed each other in battle during a civil war in Thebes.
Oedipus's brother, Creon, now rules Thebes, and he has decreed that Eteocles, who fought on the side of Thebes, be given a hero's burial, but that Polyneices, who fought against Eteocles and against Thebes, be given no burial at all and be left in the sun to rot. The punishment for burying Polyneices is death.
The plot follows Antigone's decision to defy Creon's decree and bury Polyneices, and the consequences for Antigone and Creon arise from that decision.
Like many tragic heroes in the Greek tragedies of Sophocles, Aeschylus, and Euripides, Antigone's tragic flaw (hamartia) is the sin of pride (hubris). Antigone believes that she can best decide what should happen to Polyneices's body, and that her belief in the will of the gods, as she interprets it, supersedes Creon's decree. Her pride, her willfulness, and her stubbornness eventually lead to her death.
Antigone is not the only character in the play who suffers from hubris. Her uncle, Creon, too, is prideful, willful, and stubborn.
Antigone and Creon insist on making their own way through life and living life on their own terms. They both reject good advice—Antigone from her sister, Ismene, and Creon from Tiresias, the Chorus, and just about everybody else. Neither of them will even consider the possibility that they have done anything wrong or made any mistakes in their decisions.
Antigone and Creon share one characteristic of a tragic hero—the tragic flaw of hubris.
The difference between Antigone and Creon is that Creon experiences a significant and unexpected reversal or change of fortune in his life (peripetia). Because of his decisions, his world is crumbling around him.
Antigone doesn't experience any such reversal. The course of her life in the play follows expectations—hers and ours. Nothing crumbles around her. Her life proceeds pretty much as she expected it would, and she was prepared to accept her fate from the very beginning of the play.
Creon comes to realize the mistakes he's made because of his hubris (anagnorisis), and he tries to make amends by ordering the release of Antigone from the cave where he sent her to die.
Unfortunately, Antigone committed suicide by the time the cave is opened, which causes Creon's son, Haemon, to commit suicide, which causes Creon's wife, Eurydice, to commit suicide.
Creon paid a far higher price for his hubris than Antigone did. Antigone was prepared to die from the moment she decided to bury Polyneices. Creon was not prepared to lose his entire family because of his poor decisions.
Although it might be argued that Antigone's decision to bury Polyneices set the plot in motion, and therefore Antigone is the tragic hero of Antigone, it was Creon's prideful decision to sentence Antigone to death—against the will of the gods, against moral imperatives, and against all advice to the contrary—that caused all of the deaths in the play and his own downfall.