I don't have adequate knowledge about other religions but in Islam, such sacrifices/slaughters are performed to feed those in need. I already wrote the purpose of this Eid...

to promote the spirit of sacrifice, charity, and empathy towards those who are less fortunate.

The world sees it as a mass-slaughter and cruelty and whatnot. But it's not. 74% of world population eats both veg and non-veg food and Muslim population is only 24% among which there are many who are vegetarian. I know you are not implying that but it's a hot topic that surfaces on social media during this Eid. It's much more than "something dying for something else...". Much deeper, like you said.