I just saw the movie trailer by a push of YouTube advertisement, the movie title drew my attention because I am happening working on conceptual analysis of one my project item material which with a unclear imagery of deer skull which derived from DeviantArt Twitter post. I checked and read the Wikipedia page of the movie and other Google searched pages, I don't see anything close, so, please help me for the answer of the titled question.
The Movie is titled "The Killing of a Sacred Deer" because it is conceptually based on a Greek play "Iphigenia in Aulis", according to the movie's Wikipedia page. The titular Deer is a reference to the end of the play, where the character Iphigenia, is transformed into a deer after she was killed and set on an altar. Heres the wikipedia link for the play: https://en.wikipedia.org/wiki/Iphigenia_in_Aulis