In The Oresteia by Aeschylus, how do Apollo and the Furies differ in how they interpret the bond of blood?
The Oresteia by Aeschylus is a true trilogy containing three plays that are performed in chronological sequence. In the first play, the Agamemnon, Clytemnestra hills her husband Agamemnon, in part for revenge in Agamemnon's sacrifice of their daughter Iphigenia. In the second play of the trilogy, the Choephoroi, Orestes kills his mother Clytemnestra in revenge for her having killed his father. At the opening of the third play, the Eumenides, Orestes is taking refuge with Apollo, who supports the necessity of Orestes' matricide.
The main argument between the Erinyes and Apollo is over whether Orestes is justified or culpable. The Furies argue that since Clytemnestra killed her husband, who was not a blood relative, her guilt is less than that of Orestes, who was a matricide. Apollo counters with the classical Greek theory of reproduction (which, of course, we now know to be wrong), in which the father's sperm was what grew into the child, with the mother only serving as a sort of incubator. Thus Agamemnon was Orestes' real parent and his murder needed to be avenged; matricide was a lesser crime.
Some scholars view this disagreement as reflecting an earlier, matriarchal element in the older Greek chthonic religions of which the Furies were part, later supplanted by the more patriarchal Olympian gods.