This is an interesting question, because one could argue either side of it. The story of Antigone is part of the Oedipus cycle—she is Oedipus's daughter—and Eteocles and Polyneices were his sons. After doom comes upon Oedipus, he flees Thebes to wander the countryside as a blind beggar. The city...
This is an interesting question, because one could argue either side of it. The story of Antigone is part of the Oedipus cycle—she is Oedipus's daughter—and Eteocles and Polyneices were his sons. After doom comes upon Oedipus, he flees Thebes to wander the countryside as a blind beggar. The city is left without a ruler, and it plunges into civil war as Oedipus's sons fight for control of Thebes (this story is detailed in Aeschylus's play Seven Against Thebes). Antigone opens at the end of this war, when Creon, Oedipus's brother-in-law, becomes the king.
Creon leaves the body of Polyneices unburied to serve as a warning to any remaining rebels in the city: make war on Thebes, and this will be your fate. Leaving the dead unburied was a severe taboo in Ancient Greek society, as it was felt to be offensive to the gods and prevented the soul of the unburied corpse from crossing the River Acheron into the Underworld. By threatening people with the spectacle of an unburied enemy, Creon is making a powerful statement about how he intends to deal with dissent.
Antigone, Polyneices's sister, is appalled, and her outrage is the locus of action in the play: she insists on burying her brother, despite Creon's order forbidding it, and she will not be intimidated, cajoled, or threatened on this point. Creon sentences her to death for her disobedience, although in doing so, he loses his own son (Antigone's fiancé) and his wife, who both kill themselves.
So who is "right"? Which character does Sophocles "support"? Arguably, he must support Antigone, because her death is portrayed as unjust. Creon reaps terrible consequences for his actions. However, audiences at the time would have been aware of the broader context of the story and the need for a ruler to set immovable boundaries in society after a civil war. Creon is stubborn, prideful, and harsh, but he is also responsible for an entire city that has just gone through years of upheaval. Antigone's rebellion is not simply the act of a loving sister, it is a brazen defiance of orders which risks further social unrest. It is clear from the text that she is just as stubborn and proud as Creon, but because she is the eponymous victim of the play, she is more sympathetic.
I think the obvious answer is that Sophocles "favors" Antigone because her death is decried as profoundly unjust, but it would be interesting to delve into how he shows Creon's side of the disagreement and Creon's justifications for his actions.