Why animal sacrifice in Bible?

Animal sacrifice is in The Bible because God declared that "The wages of sin are death", and "without blood, there is no remission of sin."

God is so holy, that even the smallest blemish of impurity would evaporate before Him. Therefore, if man is to come to God, his sins must have been justly punished. In order to permit man to come to God, He permitted man to "cover" his sins by sacrificing pure lambs in their place. The book of Hebrews tells us this was a prophetic shadow of things to come, where God would sacrifice the Lamb of God, Jesus Christ, a perfect human, to cleanse away the sin of man, that whosoever would take His sacrifice for their own, would be able to stand in the presence of God.

So, God's Justice, and His Love are both fulfilled in the sacrifice. The wages of sin is death - Christ died. Without blood, there is no remission of sin - The Bible says the blood of Christ cleanses us of all unrighteousness. And therefore we have confidence before God.