Antigone's tragic flaw is her fierce devotion to her family. While loyalty in itself is not a tragic error, Antigone's extreme loyalty does ultimately bring about her downfall and cause even more tragedy in Thebes.
Antigone proves her familial loyalty when, after her brothers kill each other, King Creon states that only one of the brothers is to be buried. The other brother is dishonored and must be left to rot. Antigone defies Creon's orders and buries her fallen brother in spite of the law forbidding the act. This action seals her fate and causes Antigone to be sentenced to death.