As the tragic heroine in Euripides's tragic play Medea, Medea should be a sympathetic character, but her antagonistic behavior in the play makes it very difficult for anyone to feel true sympathy for her.
In Medea's speech to the women of Corinth at the beginning of the play—before she kills her ex-husband Jason's new wife, Glauce, her father-in-law, Creon, and her own two children—Medea seeks sympathy from the Corinthian women for her mistreatment by Jason and for what she believes are inequities that she and other women suffer.
MEDEA. ... O friends! He, even he,
Whom to know well was all the world to me,
The man I loved, hath proved most evil.
... Her lord, if he be wearied of the face
Withindoors, gets him forth; some merrier place
Will ease his heart: but she waits on, her whole
Vision enchainèd on a single soul.
And then, forsooth, 'tis they that face the call
Of war, while we sit sheltered, hid from all
... thou hast this city, and thy father's home,
And joy of friends, and hope in days to come:
But I, being citiless, am cast aside
By him that wedded me, a savage bride
Won in far seas and left—no mother near,
No brother, not one kinsman anywhere
For harbour in this storm.
Medea asks the women not to betray her if she tries to "requite Jason for his sin," and they agree, but she doesn't tell them what she actually intends to do, which is to spare Jason but kill everyone else who's important to him, including their two children, in order to make him suffer the loss of everyone he loves for the rest of his life.
Whether or not the audience can find it in their hearts to have sympathy for Medea, Medea has no sympathy for any other character in the play. She's antagonistic to Jason, Glauce, Creon, and, although declaring otherwise, she's antagonistic towards her children.
The Nurse fears for the children from the very beginning of the play.
NURSE ... Methinks she hath a dread, not joy, to see
Her children near. 'Tis this that maketh me
Most tremble, lest she do I know not what.
... [to the children's Attendant] Keep them apart:
Let not their mother meet them while her heart
Is darkened. Yester night I saw a flame
Stand in her eye, as though she hated them,
And would I know not what.
Creon, fearful of what Medea might do, demands that Medea leave Corinth. Medea manipulates Creon into letting her stay in Corinth for one more day in order to prepare herself and her children for the journey from Corinth, but her true motive is to have time to commit her murders of Glauce, Creon, and her children.
Medea manipulates Aegeus, King of Athens and a lifelong friend of hers, into giving her refuge in Athens after she and her children leave Corinth.
She manipulates Jason into accepting a gift for Glauce by pretending to forgive him for the wrongs he's done to her. The gift she presents to Glauce is a robe which Medea smears with a deadly drug that causes Glauce to burn to death. Creon, trying to save Glauce from burning, is also consumed by flames.
An audience might sympathize with Medea for being torn between her seemingly justifiable hatred for Jason and the love of her children, but she nevertheless chooses hatred over love and kills her children, whose shrieks and cries of pain could be heard echoing throughout the 17,000-seat Theatre of Dionysus when the play was first performed in 431 BCE.
Medea denies Jason's request to see his children one last time before she takes them away, but she refuses.
JASON. Give me the dead to weep, and make their grave.
Medea taunts him with their dead bodies before being carried in a chariot of winged dragons to the realm of Hera, Queen of the gods, safe from human justice for her horrendous crimes.
JASON. Childless, I go, to weep and weep.
MEDEA. Not yet! Age cometh and long years.
JASON. My sons, mine own!
MEDEA. Not thine, but mine ...
JASON. Who slew them!
MEDEA. Yes: to torture thee.