Final answer:
Medea is considered dangerous due to her calculated and extreme acts of vengeance, which include the murder of her children, in response to her husband's betrayal and the unjust societal norms that oppress her. Her actions are a representation of the psychological depth and tragic consequences depicted in Euripides' work.
Step-by-step explanation:
Medea's dangerous nature in the play stems from her intelligent but ruthless actions, fueled by a sense of betrayal and injustice. Medea carefully plots revenge against her husband Jason, who has abandoned her for another woman. Her meticulous and rational planning of violent acts, including sending a poisoned cloak that led to the deaths of her rival and the rival's father, King Creon, demonstrate not only her capability for harm but also her strategic mind.
Furthermore, Medea's character is a sharp critique of the societal norms that oppress and marginalize women, foreigners, and others. Euripides uses her story to illustrate the extreme lengths to which someone might go when pushed by unjust circumstances. Medea's actions make her a tragic, formidable figure, and her ultimate decision to kill her own children is an intense manifestation of her turmoil and the dire consequences of a society that perpetuates injustice.
In the context of Greek literature, Medea's characteristics and her acts of vengeance are a powerful portrayal of human psychology and the consequences of societal norms, thereby making her one of the most complex and dangerous characters in ancient Greek drama.