The King shows hubris by thinking that he knows best and doesn't care what anyone else thinks. When he proclaims that it isn't possible for someone to disobey his ban of Polyneices being buried, Creon doesn't listen or believe the Sentry.
In Greek myth Oedipus was cursed to kill his father and marry his mother. Oedipus has 4 children: Antigone, Ismene, Polyneices, and Etecoles. He then dies and then his wife/mother dies. The family can not escape Oedipus' reputation, their nemesis.
When Antigone is arrested for burying her brother, despite it being against the law, the audience is supposed to feel pity for her because burying a sibling is seen as a moral responsibility.