Cain and Abel: Why did God accept Abel's offering and not Cain's?

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Had a very interesting discussion yesterday with some friends @ http://www.community4christ.com.

[bible]Genesis 4:1-8[/bible]
Some notes to point out:
a) Abel brought the firstborn, or first fruits, of his flock.
b) Cain was angry for God not having regard for his offering.
c) God's respond: "If you do well, will you not be accepted? And if you do not do well, sin is crouching at the door. Its desire is for you, but you must rule over it."
d) Cain's reaction: "Cain rose up against his brother Abel and killed him."

So looking at this and the noticed points, we can come to some conclusions:
a) Abel brought his first fruits of his labor, were as Cain did not. Otherwise why would Abel's offering had been noted to have been the firstborn or first fruits?
b) Cain being upset seems to me had some sort of sin in his heart before God rejected his offering. Being angry is not the 1st reaction to a righteous man.
c) God informs Cain and warns him that "sin is crouching at the door" since he did not do well. What was not done well in God's sight not exactly sure, however we can assume that Cain's heart, or faith, was not in the right place when he offered his offering.
d) Cain let sin conquer his actions by killing his brother instead of taking the warning that God gave him.

The question is, why would God take one's offering over another? Simply because of it being their first fruits?

Abel's offering was given by faith, were as Cain's was not. For Abel's faith God considered Abel to be a righteous man.

This is further explained in the book of Hebrews:
[bible]Hebrews 11:4[/bible]
So what is to be learned from the story of Cain and Abel?

God knows your heart and where your faith is. If your faith is right with God, He will count you as righteous. And even though bad things may happen to those that love God, we can take comfort in that we know that God is always with us and will never forsake us. Even after this body died, God still blesses us.

Grow in your faith, and see what God will do in your life. For God blesses those who love Him.

[bible]Psalm 37:21-22[/bible]
[bible]James 1:12[/bible]
[bible]Psalm 5:12[/bible]
Be blessed and be a blessing.

God bless,
Johnathan