Why do Greek tragedies have masculine female characters?

Greek tragedies often have masculine female characters because they were designed to shock their audiences. The Festival of Dionysus was supposed to be a cathartic experience for the Athenian audience, and having women do brave or evil acts helped the population release some of the tension that had built, like a pressure valve. The plays were supposed to engage with the audience and create negative emotions so they felt them at the correct time and place, and seeing Medea commit infanticide or Antigone bury her brother's body would have allowed the audience to feel angry or disgusted or shocked at the appropriate time.

They also reminded the audiences that women had to be controlled. Greek women were supposed to be restrained by the kurios, who was their husband or their closest male relative. This man was in charge on ensuring that the woman in question behaved properly and punished her when she was improper. These plays reminded the mostly male audience that women needed a strong kurios, or the results were disastrous for their family, or oikos, and Athens as a city, or polis.