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 Sophocles refers 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.