Creon abuses his power by refusing to allow Polynices to be mourned or buried. He does not want to honor Polynices by giving him a burial, and he also wants to maintain control. His abuse of power comes from his desire to make what he sees as the needs of the state supersede divine law.
From Creon's perspective, Antigone leaves him little choice. She has openly defied the law and makes no attempts to deny it. She leaves Creon no choice but to execute her, even though he is not especially eager to execute his son's fiancée. But Creon's desire to make the state supreme, and to prevent any challenge to his personal power, leaves him no choice but to follow through with his threat.
Antigone, for her part, wants to assert that kinship and honor are more important than preserving personal power. Her love for her brother transcends Creon's authority and is doubly dangerous: first, because it leads to her open defiance of Creon's authority, and second, because it calls into question the moral basis for Creon's rule. Creon's decision to bury Antigone alive is an exercise in futility. He may be able to literally cover up Antigone, but he cannot disguise the dishonor that comes to him from permitting the desecration of Polynices's corpse.