Final answer:
Medea kills her children mainly out of revenge and betrayal after her husband Jason abandons her. She also rationalizes the deed as a fear of the future. Her actions, although horrific, are portrayed as calculated rather than the result of mental illness.
Step-by-step explanation:
The reasons Medea gives for killing her children are rooted primarily in revenge and betrayal. Medea's actions stem from a deep sense of betrayal after her husband, Jason, leaves her for another woman. The killing of her children is a calculated act of retribution directed towards Jason, as she believes that by depriving him of his offspring, she will inflict the maximum amount of suffering upon him. This act is Medea's ultimate revenge for Jason's abandonment, a point accentuated by the historical context whereby children are seen as a man's legacy.
In addition to the primary motive of revenge, the act also demonstrates Medea's attempt to protect her children from a potentially bleak future or retaliatory harm from their father's enemies. Within the play, Medea debates the consequences of her actions, weighing the horror of the act against the perceived benefits of protecting her children from a life of shame and dishonor. This underscores the importance of reputation and lineage in ancient Greek society.
Lastly, while Medea does exhibit behavior that modern audiences might interpret as signs of mental illness, in the context of the play, her rationale is depicted as cold and calculating rather than stemming from a loss of sanity. Importantly, her actions also include sending a poisoned cloak to her rival, further illustrating her methodical and punitive approach to revenge.