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And almost all things are by the law purged with blood; and without shedding of blood is no remission.
I used to think that God did not approve of Cain's sacrifice because he did not offer up animals and because there was no shedding of blood, there was no remission of his sins.
But now, looking at the context of this scripture, I think differently.
The context is this: Abel tended to the flocks, while Cain tilled the ground. But here, we can see in [Genesis 4:7] that if we do well, we shall also be accepted. Whatever we do, we have to do with a spirit of excellence and whatever we offer to the Lord has to be the best. Obviously from verse 7, we can see that Cain did not offer his best and that is why his offering was not accepted.
You can also see that "sin lies at the door" which to me implies that his heart was not right. You can also see that from the subsequent verses, out of the anger of his heart and because he harboured sin in him, he exacted vengeance against his brother and killed him.
God knows the condition of our heart. When we give an offering to Him, we give with a willing heart and we give Him our best sacrifice.
We can also obtain revelation from the Epistle to the Hebrews:
By faith Abel offered unto God a more excellent sacrifice than Cain, by which he obtained witness that he was righteous, God testifying of his gifts: and by it he being dead yet speaketh.
Again, it was the condition of our heart that God accepted. Abel offered a sacrifice by faith.
and the passage in Hebrews continues with this verse
But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.