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SeptemberMorn said:
Adam and Eve's sons, Cain and Able, also made sacrifices to God. You'll read about it if you haven't already. Able's sacrifice was accepted because he had pure intentions. Cain's sacrifice wasn't accepted, shown by the fact that the smoke from his fire didn't rise but went down, because he had resentment towards Abel in his heart when he made his sacrifice.

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I think that animal sacrifices were only required during the Old Testament (?)... but why did God want them anyway? God is supposed to be all-powerful, omniscient, etc; why should sacrifices have pleased him, especially when they were of innocent animals such as lambs which had never in any way harmed Him?