In order to understand Antigone’s motivation for giving her brother a proper burial, one has to understand what has happened before the events of this play. Sophocles wrote about Oedipus, Antigone’s father, in two previous plays—both of which feature Antigone in small roles. Oedipus, of course, is a cursed individual, and that curse is passed on to his progeny. Antigone already knows this from the beginning of the play, but she resolves to do the right thing anyway.
According to Ancient Greek customs, denying someone a proper burial would offend the gods and prevent one’s soul from achieving peace in the afterlife. Antigone, knowing she is cursed anyway and feeling a little guilty about not making it to Thebes in time to intervene before both of her brothers are killed, feels responsible for Polyneices’s post-mortem fate.
She also doesn’t care much for Creon and his self-righteous attitude, and I think a part of her just wants to show him that she can do what she wants. Antigone is loyal to her family and the gods above all, which is why she is determined to give Polyneices a proper burial. Antigone knows that if she doesn’t step up to do it, no one will.