It is hard to construct a defense for Medea. Euripides portrays her as a monster—he writes her as selfish, vengeful, and evil. The murder of her children is seen as unforgivable. However, I think there are some things you can point out that help build empathy for Medea, though they might not be good enough to stand as a “defense” of her actions.

In the play, Medea is being cast off by Jason in favor of a woman who is better connected. To understand the level of this betrayal, there needs to be some background. Medea has saved Jason more than once, and he would never have succeeded in any part of his quest without her. She has given him everything: her undying loyalty, her body, her magic, and her life. The two don’t marry in the conventional/legal sense but instead make an oath to the gods, which can be considered more binding than a simple legal marriage. To understand the extent to which Medea sacrifices to be with Jason, we can read her monologue early in the play,

You have this city and your father's home,

enjoyment of life, and the companionship of friends,

but, alone and without a city, I am abused

by my husband, carried off as plunder from a foreign land,

I have no mother, no brother, no relative

to offer me a safe haven from this disaster. (252-257)

Medea considers leaving Jason after he has told her that she will be exiled, but she feels like divorce is not enough. She asks the audience to understand her side. She shows them that she has nothing but Jason and that she has abandoned everything to be with him. Her sacrifice is the driving point of her revenge and escape at the end of the play. She might seem insane in her choice to kill her children, but given the circumstances and time when the play was written, it makes some sense why she does it.

Jason, knowing that she will be poor and abandoned in exile, offers Medea money. This solidifies her anger at him and drives her to murder the princess and king later in the play. She tells him,

We will not be making use of your friends;

I will not take anything from you; don't give me anything.

The gift of a bad man brings no pleasure. (615-618)

Her unwillingness to take the money is foreshadowing the fact that she doesn’t anticipate having to care for the children later—but also shows her complete break from Jason. She is abandoned, and she knows that her relationship with him is done.

Medea seeks revenge, but her choice to murder the children is more complicated. Jason had taken everything from her—Kyrios (her household, when she abandoned her father), Oikos (all familial relationships, especially when he tries to leave her), and Polis (her relationship to her country, which she has to give up when she flees). She exists in Corinth as a Xenos, a stranger with no legal standing and suspicions from everyone that lives there. His choice to break his oath cost her everything, and she takes everything from him in turn.

Medea kills the princess and the king, alienating Jason in the city, and then she kills the children. She says she does it to “protect” them from the citizens of Corinth, who she believes will kill them if she doesn’t. However, she admits to Jason that she did it to spite him. She leaves him without the ability to bury their bodies, and he has nothing at the end of the play—not even the gods will hear him because he is an oathbreaker. His being an oathbreaker is probably Medea’s only defense that works in terms of the mythology and play.

It is interesting to note that Medea never faces vengeance or curses from the gods for her action in murdering her children. Typically in Greek Mythology, it would violate cultural norms and “the will of the gods” to do something so terrible. However, Medea gets a pass—she even flees in a chariot given to her by her grandfather, Helios, showing that the gods are helping her. The reason Medea doesn’t face punishment is that the gods excuse her actions in light of Jason’s breaking his oath—they see his swearing on them and then recanting as worse than her taking the lives of her children.

Medea’s actions are awful. However, she never led us to believe that she was a “good” person. She questions the ties of family and breaks social convention repeatedly in the story. She betrays her father, saves the hero, and even fits into the role of mother and wife despite hating them. Her actions are predictable given that she has no one and nowhere to go. The children are a tie to Jason, and she kills them to end his life as much as he ended hers. Ultimately, she claims it was like an eye for an eye—she was making him suffer as she had. Most people would argue that she goes too far in her revenge, but you could say that saying one step in revenge is too far over another is splitting moral hairs.

Ultimately I think the best defense of Medea’s actions is to say that she doesn’t care about good or evil—the moral definitions of society don’t mean anything to her. She exists outside of society, so judging her by what society says is good or bad is meaningless. Instead, she repays Jason for the evil he has done to her by forcing him to live with unbearable pain, and the action she takes fulfills her ambition. To us, it is evil, but to her, it is justice.

Medea is humiliated by Jason's new marriage and her pride will not quietly suffer this situation -- she is determined to seek revenge.  While it would be easy for her to kill Jason, she actually makes some sense when she decides to let Jason live the misery she can invoke!  She kills his new bride.  But she knows that that action is not going to go unpunished and that both she and the children are now going to be treatened by those loyal to Creon.  In Episode 5 she is vacillilating about the decision to kill the children, but part of her decision to do so is, in her mind, to protect them.  She says, "This shall never be,  that I should suffer my children to be the prey of my enemies insolence."  After knowing that the princess and Creon are dead she says, "as quickly as I may to kill my children, and start away from this land, And not, by wasting time, to suffer my children to be slain by another hand less kindly to them."  She is suggesting that it would be better to kill her children herself than to have them killed by her enemies.  While this does speak to her own pride, she is trying to justify her actions.  I don't think this makes the action defensible, but it makes some sense to Medea.  She does kill them to punish Jason, but it was not that simple for her.

Personally, I don't think that Medea's actions can be defended.  She doesn't suffer from a predetermined fate like Oedipus who from birth was slated for a life of misery and violence. While the audience would sympathize with Medea because of Jason's betrayal and humiliation of her, there is simply no justification for her murdering her children or Creon, who actually tried to help her near the play's beginning.

Even a plea of insanity would be difficult to prove because Medea is cunning and develops an elaborate plot to kill Creon, his daughter, and her own children.  The chorus repeatedly tells her not to go through with her plans, and she wavers later in the play in regards to her children's deaths; so she is obviously cognizant that her plan is immoral.