Why does Creon fear Medea in Euripides' Medea?
Creon fears Medea because he senses that the latter will take revenge upon him, his daughter Glauce, and his new son-in-law, Jason (formerly Medea's husband). Above all, Creon fears that Medea will reserve her greatest malice for Glauce, his daughter.
As he speaks to Medea, Creon also reveals his deep distrust of silent, clever women. It is clear that he prefers women to be overt in expressing their emotions; he is adept at responding to such displays of feminine wrath. However, a silent woman who keeps her emotions under control is to be feared because her plans for evil are hidden from him. Creon believes that Medea is a silent, dangerous woman. Therefore, he resolves to banish her from the country.
However, the wily Medea is not to be bested. She placates Creon by telling him that he acted in "good sense" when he married Glauce to Jason. By speaking thus, Medea appeals to Creon's masculine pride. When Creon holds his ground, Medea appeals to Creon's paternal inclinations. She suspects that Creon will not deny her the ability to make provision for her children's future.
Accordingly, she requests an extra day in Corinth, telling Creon that it is for her children's sake. Creon is loathe to humor her, but his compassionate nature gets the better of him. It is an unwise decision, of course, because Medea aims to turn Creon, Jason, and Glauce into "corpses." In fact, we are told that she means to use poison to murder all three.
Her first victim is Glauce. Medea sends her children with two gifts to Glauce: a coronet and a dress. Medea tells Jason that she sends the gifts so that Glauce will advocate on her children's behalf before Creon. With tears, she manages to convince Jason that her only care is for her children; she claims she does not want them to be exiled along with her. Jason permits his children to deliver the gifts to Glauce. He fails to realize that the gifts contain powerful poisons.
Glauce later dies when the dress corrodes her skin and the poisoned, eerily inflamed coronet pierces her head, causing her skin to bleed and her flesh to dissolve. Meanwhile, as Creon embraces Glauce, the poison seeps into his own skin. Both father and daughter suffer horrible deaths.
Immediately after, Medea kills her children. Her actions give her little pause for concern. She is pleased that Jason will suffer unimaginable grief when he discovers the deaths of Creon, Glauce, and his children. Medea's actions demonstrate that Creon was wise to fear her.
In Euripides' Medea, the title character discovers that her husband Jason is going to divorce her and marry the daughter of Creon, who is the king of Corinth. Initially, Creon decides that Medea should be exiled as soon as possible.
The reason for this is that Medea's reputation precedes her. She is skilled in the arts of dangerous magic. By the time Medea reaches Corinth, she already directly or indirectly brought about the deaths of several people, including her own brother, Absyrtus, and the king of Iolcus, Pelias.
Given Medea's past, plus the fact that Medea will be enraged because of Jason's abrupt and unjustified divorce of her, Medea is likely to be a very dangerous woman. Moreover, Creon has already heard that Medea has been making threats against his daughter:
"Many things lead me
to this conclusion: you're a clever woman,
very experienced in evil ways;
you're grieving the loss of your husband's bed;
and from reports I hear you're making threats
to take revenge on Jason, on his bride,
and on her father." (Ian Johnston translation)
Unfortunately for Creon, Medea persuades him to allow her to remain in Corinth one more day. That is all the time Medea needs to orchestrate the murder of Creon's daugther. Creon himself is also killed in this plot.