Before we consider Medea's choice to use violence as a solution to her situation, we need to take a very quick look at another Greek play, Oedipus Rex. In Oedipus Rex, the playwright Sophocles gives us a flawed but noble hero who ultimately chooses to punish himself rather than others. Oedipus represents the kind of character Aristotle referred to as the kind of hero who accepts responsibility for his actions, thus showing us a "better" way, that we can be better than we think. Oedipus reveals his heroic side. This is what heroes do, accept responsibility for their actions but not Medea. Medea has been wronged no doubt because Jason has discarded her for a younger woman. Medea's response, however, is to murder her sons, strangely, both in order to punish Jason and to protect them from Jason and his new queen. She feels powerless so she chooses a violent way out. She shows us the consequences of Jason's treachery but in ways that hardly seem defensible. In the end, her violent response seems to suggest that life is rarely just. It is a troubling and in some ways unsatisfying ending to be sure. In fact, she escapes and is not punished for her actions--except in the loss of her sons, which is ironic indeed. Unlike Oedipus, however, she is perhaps more complex and more human, foreshadowing or paving the way for the complex heroes we will find some in the plays of William Shakespeare.
The violence contributes to the themes of revenge and passion. It's true for Medea that there is a thin line between the love and hate she feels for Jason. Her passionate love for him leads her to give up everything to be with him, including killing her own brother. Her excessive love for Jason quickly turns to deep anger and hate, so much so that Medea is willing to kill her own children just to hurt Jason. She loses all sense of reality and allows her passion for revenge to control her. Breaking the law means nothing to Medea just as the warnings of the chorus fall on deaf ears. Her tragic flaw is her inability to exhibit her emotions moderately instead of excessively.