Animal Sacrifices

As an animal lover I always found it difficult to understand why the God who created animals, would command the sacrifice of them. It seemed incredibly cruel to me.

Then I read verses like the following by David in Psalm 51:16-17.

For You do not desire sacrifice, or else I would give it; You do not delight in burnt offering. The sacrifices of God are a broken spirit, A broken and a contrite heart— These, O God, You will not despise.

What? That really confused me. Did God want sacrifices or not?