According to Aristotle's definition, a tragic hero is a noble figure whose desire to do good is affected negatively by their tragic flaw. This tragic flaw can bring about the hero's downfall. In the case of King Arthur, there are several qualities that could be said to be his tragic flaw. One is that Arthur, by way of his upbringing, is innocent and therefore naive. He has not lived among nobility until he suddenly is made king as a young man, and so he does not know of the sometimes capricious ways and corrupt dealings of the monarchy. This naivety makes it hard for Arthur to understand he must plot to thwart Mordred's plan to usurp the throne. He merely wants his son to acknowledge their bond, but Mordred was brought up to hate his father. Arthur is deeply conflicted about the situation.
Another tragic flaw in Arthur is his loyalty. He is so deeply loyal to both Lancelot and Guinevere that even when they both betray him, he cannot act in his proper role as king and punish them appropriately. He is also loyal to Merlin even when Merlin does not always act in Arthur's best interests. This loyalty causes him to forgo his proper duties as king.