Describe the rationalization process of the Erinyes in "The Eumenides" by Aeschylus.

The Erinyes are the Furies and usually consist of three deities of destruction and vengeance. They are understood to be advocates for the dead.
In the play, the Erinyes want Orestes to pay in blood and suffering for his mother Clytemnestra's murder. The Erinyes/Furies rationalize their thirst for blood vengeance by referencing the ancient Greek codes of blood-pollution. Because Orestes killed his mother, they claim that he has polluted his legacy; the Erinyes emphatically argue that this kind of familial pollution can never be erased. On the other hand, the Erinyes do not interest themselves in pursuing Clytemnestra for killing Agamemnon (her husband) because the two are not blood kin.
According to the Erinyes, guilt can only be effaced through the execution of equivalent violence on behalf of the victim. Furthermore, the Erinyes maintain that Orestes deserves to be driven mad for his matricide; they hound him mercilessly with the miasma of Clytemnestra's dead spirit. The dead spirit is believed to be a polluted presence, and therefore poses a danger to the larger community. Here, the Erinyes reference the ancient Greek belief that murder can render a perpetrator insane. During the trial, the Erinyes stress that Orestes can never remove the blood-taint of his matricide, and they pronounce him unclean and unworthy to perform any religious rituals in his city. Essentially, the Erinyes reject the claim that anything other than blood atonement can purify Orestes.
Sources:
Inner Purity and Pollution in Greek Religion: Early Greek Religion, Volume 1 by Andrej Petrovic, Ivana Petrovic.
Restless Dead: Encounters Between the Living and the Dead in Ancient Greece by Sarah Iles Johnston