This is an excerpt from “Speaking Christian: Redeeming Christian Language”
The bible contains language about impurities you could acquire that needed to be removed through sacrifice. Impurity is not the same as sin, sometimes there is an overlap, for an example when a woman gave birth to a child she became impure for forty days, at the end of forty days she would become pure again not simply through the passage of time but also through a sacrifice. This is talked about in Luke’s birth story of Jesus. If you were a well to do woman the sacrifice might be a lamb or a goat, if you were a poor woman it could be something as simple as a dove. Notice that the sacrifice to remove an impurity here really has nothing to do with sinfulness, even though these are sometimes referred to an sin offerings in some English translations of the bible. There’s nothing sinful about giving birth, the purification offering has nothing to do with the forgiveness of sins.
The last point about sacrifice, in all of these animal sacrifices, in the old testament, in the temple of Jerusalem there was never the notion that the people offering the sacrifice really deserved to be put to death but that god was willing to take it out on the sheep. This idea is just not there. The root meaning of sacrifice or in the Latin, sacrificium it means to make something holy or sacred by offering it up to god. Returning to animal sacrifice, when you sacrifice the animal to god the animal becomes holy or sacred and is simultaneously a gift to god. In most cases of sacrifice the animal came back to the people, now burned and cooked as meal. Having a meal is implied in the meaning of sacrifice. You make a gift to god and it comes back to you as a meal except that now it is a meal with god. By a portion being burned and sent up to god you have shared with god and are participating in a form of communion. This adds a nuance to Eucharistic liturgy, it’s about offering a gift to god and then sharing a meal with god. That is the root meaning of sacrifice, to make something holy by offering it up to god.