Does the Bible teach that we should sacrifice animals?

No, it does not. Christians acknowledge that Jesus put an end to the tradition of sacrificing animals that was being carried out in God’s name by some Jewish sects in his time and by their predecessors. He brought a new covenant and instead told us to break bread with each other as an act of fellowship and remembrance of him. If you look into the issue further, you’ll see that even the Old Testament prophets likewise sought to end the practice of animal slaughter, stating firmly that God does not nor ever desired animal sacrifices. Jesus similarly taught that what God wants is “mercy, not sacrifice.” For a more detailed explanation, read Mercy and Animal Sacrifice.