Great responses, guys!
I heard Scott Hahn give a good analogy of why God instituted the Sacrificial system at Mt. Sinai.
The Jews had just returned to the idol worship that they had taken part of in Egypt. God was punishing them by making them sacrifice the very animals that they had worshiped.
It’s like a man who has a drinking problem and his wife has had it “up to here”. She wakes him up early one morning, while he’s still suffering from a nasty hangover, and gives him a bottle of scotch and a hammer. She tells him to destroy the bottle or she will leave him. After destroying the bottle, the man thinks its over and his wife has forgiven and forgotten.
The next morning, the man is greeted yet again by his wife with another bottle of scotch and a hammer and given the same ultimatum. This continues every day for the rest of his life.
By this sacrificial system, Israel was daily reminded of their transgressions against God in the Dessert!