Antigone, as the daughter of Oedipus, has lived a challenging life, but she is strong and determined to do the right thing, which seems to be a characteristic she shares with her father who was determined to find the truth, even when the truth ended up destoying him. Antigone is determined to see that her brother is buried in a proper ceremony, even though it is a direct violation of the orders given by her uncle, King Creon, who declared him a traitor and and a criminal to the state. Antigone knows that the laws of the gods are always more important than the laws of man, and she refuses to apologize for her actions or back down in any way. In th end, she commits suicide rather than betray what she knows to be right. It is by these actions that Creon sees the error of his ways and tries, too late, to save Antigone. Both the Oedipus stories and this one illustrate the theme of hubris, which by a strict Greek definition is excessive pride -- pride that suggests that a person thinks they know better than the gods. Oedipus thinks he can out-wit the oracle of Apollo, and Creon thinks that he can change the laws of buriel. Both men live to suffer with the knowledge of just how wrong they are, thus the series of plays in total illustrates variations on that theme of the dnager of hubris.
Well, basically he wrote it to complete the cycle of plays of the Oedipus story, of which Antigone is the last. So, you could say that it was a necessary thing to do in order to "finish the drama". The plays back then were completed in series, one following the other. So, Antigone is one of those series of plays, only this one (which is about the conflict of duty versus fate) is at the end because the theme denotes that the protagonist is about to meet a fate that cannot be controlled, hence leading to the end of it all.