A good part of the emotional power of this play comes from the fact that Medea does NOT let the norms of Greek society or her position in it define her life. The play opens with the news that Jason has decided to leave his wife, Medea, and his two sons, in order to marry the princess of Corinth. He is doing this, he claims, to better secure his family's position in Corinth. Medea is furious that all she has done for Jason has been cast away, and that she is left with no recourse in the matter. Once she gets past her despair, she quickly moves into revenge mode, and that is when she gets dangerous. Jason may "hold all the cards" in what he decides to do with his life, but Medea is NOT going to be kept down to be pitied as the poor pathetic woman left behind. Her pride will not allow her to stand by and be mocked for what Jason has done to her. She makes it abundently clear to the Chorus that she plans to "pay my husband back for what he has done to me."
Her plan starts in small part when she meets up with Aegeus. Aegeus is the King of Athens and would be capable of protecting her there, but he doesn't make it that simple. As a patriarchal leader, he makes the deal that he will protect Medea if she arrives in Athens, but he will not help her get there. He only does this in exchange for magical help from Medea to help he and his wife concieve an heir. He clearly asserts his authority in this situation.
Once Medea has secured safe harbor, she goes about her plan of revenge. It is a two-fold plan: first kill the princess with a magical gown, then kill her own children. It is a shocking, outrageous plan, but she is determined that Jason should have life-long suffering for what he has done. Killing him would be too easy.
In traditional Greek society, women were essentially powerless in a male dominated society. Jason actually tells Medea that she should be happy for what he has done. Medea, breaking the mold for women, takes her fate into her own hands and determinedly does what she deems that she has to do.