Medea is laced throughout with the theme of exile. All the characters relate to the motif. Some, like Medea, have been banished from their homes; some are the ones doing the banishing. The theme of exile would have resonated strongly with Euripides's audience of ancient Athenians. Their city-state was their lives. The thought of being cut off from it and cast out into the wilderness would have been terrifying.
Jason's betrayal of Medea is worsened by the fact that she forsook her father and homeland for love of him.
Medea's banishment is her own fault, as her threats of Creon and his daughter are what cause it.