The movie is full of references to Greek myths apparently. The title itself, the four stages of sickness, etc. What are the other references that you could name and what known myths do they refer to?
Killing of a Sacred Deer is loosely based on Greek myths recorded in plays from Homer, Aeschylus, and Euripides, and seems to be based on the myth of King Agamemnon murdering his daughter, Iphigenia.
This Vulture piece gives a good run-down of them.
This quote from the article explains where the film’s title comes from.
However, in Euripides’s Iphigenia at Aulis, the reason for Iphigenia’s sacrifice is made more explicit: Agamemnon accidentally killed a sacred deer that belonged to Artemis, and she requires blood in return.
(BTW: If you have questions about the myths, best ask them in the Mythology/Folklore exchange.)