Genesis 4:1-7 - Why was Abel's offering accepted and Cain's offering rejected?

In Genesis 4:1-7 we have the story of Cain and Abel bringing offerings to the Lord.  The Bible makes it clear that Abel's offering was accepted by God while God rejected Cain's offering. Yet there is no details or explanation given as to why Cain's offering was rejected. 

We must start with the truth that both Cain and Abel knew what God's requirements were for an offering.  While the Bible text doesn't say this explicitly that God told them what the requirements were it is clear that Abel does the right thing and Cain doesn't that they both knew what the requirements were from God.

Hebrews 11:4 sheds some new light on this whole episode.  It says that by faith Abel offered a better sacrifice than Cain and by that acceptable sacrifice God commends or testifies to Abel as righteous.  It further says that the testimony or commendation of Abel's righteousness was that God accepted Abel's gift or sacrifice.  It is also possible that the bringing of the right sacrifice in faith actually caused righteousness to be credited to Abel.

By contrast, Cain was not righteous when he came with his offering and therefore did come before God in faith and so his offering was rejected.  Because Cain was not righteous and did not come before God in faith it suggests that Cain didn't believe what God had told him about the requirements of the offering he was supposed to bring.  It seems Cain brought what he chose to bring rather than what God had told him to bring.  All of this meant that Cain continued in his condition of unrighteousness after his offering was rejected.

As to the offering itself both animal sacrifices and grain offerings were a part of the worship ritual of the Israelites so both were acceptable depending on the reason for the offering.  In this case God may have told both Cain and Abel to bring a first fruits offering which Abel did and Cain didn't or God may have told them to bring an animal sacrifice which Abel did and Cain didn't.  The point is that Cain did not believe whatever God told him to bring and therefore was rejected by God.