must always be accounted for, because fate itself is such a critical theme within the entirety of Ancient Greek mythology and epic storytelling.

That being said, I don't think fate plays as central a role in Antigone as it does in stories such as the myth of Oedipus. In that case, the storyline is actively shaped by prophesy, with attempts to supplant fate ultimately resulting in fate's fulfillment.This first happens when Oedipus was abandoned to die, and later when he relocates to Thebes.

Antigone is different, however, in that its characters exhibit far more agency in shaping their particular tragedies. In this case, the tragedy emerges out of a conflict between Antigone and Creon. Antigone defies Creon's law, making a stand for principle and drawing Creon's wrath in the process. She is aware that Creon has forbidden her from burying her brother, but she does so anyway in defense of traditional piety and the rites due to the deceased.

Similarly, Creon chooses to assert his political authority, sentencing her to death rather than showing mercy though he will later change his mind, but only when it is too late. In this case, the tragedy is shaped by this clash of personalities, and the choices these characters have made.

In Antigone, as with all Greek plays, the overall fate of the characters is decided by the gods in advance. However, that still leaves each individual with the ability to exercise free choice in how they will respond. Some choose to defy their fate, displaying great hubris, or overweening pride. Others will calmly accept their fate, taking whatever life throws at them and managing as best they can.

In the case of Antigone, she has chosen to exercise her free will, irrespective of what fate has in store for her. In defying Creon's express orders, she undoubtedly displays immense courage. Yet at the same time, she is showing great pride, and it is no surprise that Antigone is admonished by the Chorus for her transgressions. Antigone may be a heroine, but her heroic status is ambiguous, to say the least.

In any case, the method of Antigone's death is what really matters here. One could argue that suicide is the ultimate act of free will. It is Antigone's fate that she, like everyone else, will eventually die. However, what's not fated is precisely how that will happen. In choosing to kill herself, Antigone is exercising her free will to the utmost in a final act of defiance against Creon and the terrible fate he has in store for her.

It seems that Sophocles wants to make the point that Antigone made choices leading to her death while Antigone herself wants to justify her choices as being the direct result of her parents' sins.

There are many places all throughout the play in which Sophoclesrefers to choices and decisions, showing us that this is ultimately a play about choice rather than fate. The first place that choice is mentioned is when Ismene makes the choice to not assist Antigone in burying their brother but rather to yield to authority. After this choice, Antigone says that she would not let Ismene help her now even if she changed her mind, as we see in Antigone's line, "[I]f you change your mind now, I would not have you do it with me" (69-70). The differences in Antigone's and Ismene's choices are again referred to when Antigone argues that some people think Ismene's decision was wise; some think Antigone's decision was wise, as we see in Antigone's line, "You seem clever to some, I to others" (573). Even the chorus refers to Antigone's choices in pointing out that she is as stubborn as her father and like her father does not know how to bend to authority (485-487). In addition, the chorus argues that her decision was a poor one in the lines:

You went forward far too boldly
and crashed into the lofty pedestal of Justice. (859-861)

Hence, Sophocles does a great deal to point out that Antigone's death is due to her own choices.

However, wanting to incite the chorus to empathize with her, Antigone makes the argument that she is cursed and that she is paying for the sins of her parents. She refers to herself as dying "accursed, unwed" (873). However, the chorus argues back that her "self-guilding anger destroyed [her]," rather than any sins of parents. The chorus does say earlier that she is "paying for [her] father's crime," but in light of what else the chorus says, they seem to be saying that Antigone is needlessly paying for her father's sins with death brought on by her own decisions.

Hence, it seems that we can make the case that Sophocles is primarily arguing that Antigone's decisions led to her death rather than fate or a curse from the gods. 

An element of the fate versus free will dichotomy can be seen in the decisions that characters make and the way that those decisions lead to a very definite fate that results in tragedy. Although fate versus free will is a theme that can be seen much more clearly in Oedipus Rex, in Antigone it is expressed through the choices that characters make and what those choices signify, which result in no uncertain terms in tragic fates for all the characters. This is of course most clearly shown in the central character, Antigone herself. Note how she describes Creon's edit in the opening scene to Ismene:

Whoever

disobeys in the least will die, his doom is sealed:

stoning to death inside the city walls!

The phrasing of "his doom is sealed" is particularly resonant of fate: Sophocles is making it very clear that actions have definite consequences, and if Antigone chooses to bury her brother's corpse, she will die a premature death. However, for Antigone, there is no choice. Her character and her determination to see her brother honoured before the gods means that she will die, no matter what anybody says. In the same way, Creon's determination to show his power by making the edict in the first place dooms him to a very unhappy life, as it results in Antigone's death which in return results in his own son's death. In each of the main characters, their own qualities seem to doom them to a definite fate that they have no control over whatsoever.