The conflict in Sophocles' Antigone arises because of the opposing beliefs of Creon and Antigone.
Creon, who places duty to his land and people above anything else, passes a law that Antigone's brother who had turned a traitor, would not be honoured with a burial and that his body be left in a state of shame.
Antigone opposed this, placing familial ties above the laws of her king and land.This conflict between the two spirals into an ugly and vengeful outcome.