Why did God accept Abel's offering and disapprove of Cain's offering in Genesis 4?
The Bible says in Genesis 4:4–5 that “the Lord looked with favor on Abel and his offering, but on Cain and his offering he did not look with favor.” The book of Hebrews gives us some help with your question. The writer to the Hebrews says, “by faith Abel offered to God a more acceptable sacrifice than Cain” (Heb. 11:4). The issue was a matter of heart and inner attitude. Abel offered his sacrifice in faith, giving God his best, the first of his flocks and the fat parts. Faith did not motivate Cain in his offering. Cain attempted to approach the Lord in his own way and on his own terms, presenting an offering to the Lord that was born in self–righteousness, self–confidence, and unbelief. We must approach the Lord through faith in Christ, on God's terms and not ours.