My friend Maya commented, "I have not come across any theory why societies tend to abandon (human sacrifices) as they progress."
World-wide many societies ended human sacrifice because;
“Sacrifices and offerings, burnt offerings and sin offerings you did not desire, nor were you pleased with them”—though they were offered in accordance with the law. Then he said, “Here I am, I have come to do your will.” He sets aside the first to establish the second. And by that will, we have been made holy through the sacrifice of the body of Jesus Christ once for all." Hebrew 10:8-10
But, why did the Ancient Greeks give it up? In Ancient Greek tradition, a sacrifice is a "diaz"; a community feast. Famously, the Olympian gods objected to eating human flesh at Tantalus' home. (Apollodorus, Bibliotheca E2. 1 - 3 ).
Could the taboo against human sacrifice reflect a trend in divine diet? In the Golden Age the Titans drank wine and ate meat with mortals. But in the continuing effort to separate themselves from mortals the Olympians dined separately from mortals and exclusively on ambrosia and nectar. So much so, that the youngest of the Olympians could not eat meat.
"Next glad-hearted Hermes dragged the rich meats he had prepared and put them on a smooth, flat stone, and divided them into twelve portions distributed by lot, making each portion wholly honorable. Then glorious Hermes longed for the sacrificial meat, for the sweet savor wearied him, god though he was; nevertheless his proud heart was not prevailed upon to devour the flesh" HH to Hermes
Following the gods example, men fasted to be purified for sacred rituals like the Eleusinian Mysteries in honor of Persephone whom like Christ returned from the dead.
If there is any sort of taboo on roast beef how much more so on human flesh?