1-2 Now Adam knew Eve his wife, and she conceived and bore Cain, saying, “I have produced a man with the help of the Lord.” And again, she bore his brother Abel. Now Abel was a keeper of sheep, and Cain a worker of the ground.

3-5 In the course of time Cain brought to the Lord an offering of the fruit of the ground, and Abel also brought of the firstborn of his flock and of their fat portions. And the Lord had regard for Abel and his offering, but for Cain and his offering he had no regard. So Cain was very angry, and his face fell. 6-7 The Lord said to Cain, “Why are you angry, and why has your face fallen? 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.” Genesis 4:1-7 English Standard Version

The story of Genesis now moves to the descendants of Adam and Eve. The apostle Paul stated this truth when he preached to the intellectual people of Athens and said: “God made from one man every nation of mankind to live on all the face of the earth.” (Acts 17:26) But why do you think no mention is made of any daughters born to Adam and Eve here, and not until Chapter 5:5?

Many people say it's because the Bible is a 'male chauvinistic' document. Woman don't matter. But that's not true. The simple reason is because the promise of someone who would ultimately crush the serpent (Satan) was that it would be a male descendant of woman. So Eve saw the birth of her first male child as being 'with the help of the Lord'. It's possible that she and Adam hoped this might be the one God was sending to rescue them. The Gospel writer Luke picked up on this when he wrote of Jesus “Jesus, when He began his ministry, was about thirty years of age, being the son (as was supposed) of Joseph.” Luke then traces the male lineage of Christ all the way back through history and ends with the words “the son of Enos, the son of Seth, the son of Adam, the son of God.” (Luke 3:23-38)

Another question people ask is “why did God have regard for Abel and his offering, but not for Cain and his offering?” What are your thoughts on that?

The Bible doesn't tell us so we can't be dogmatic about why we think this happened. Some hold the view that Abel had realized that because God said disobedience would lead to death, it would need a death to make atonement, and so he sacrificed a lamb. The Bible says God had regard for Abel, and for his offering. It may be that he was already showing the spirit of repentance.

The description of Cain's response to God's rejection sets the tone for the response and struggles that future generations would show when things don't go their way. (And especially if God does not accept their way of serving Him.) He became very angry with God. Is that not true still of people who hate it when God does not approve of their lifestyle choices? And we are told 'his face fell'. That has ever since been a way to describe someone who has experienced a huge let down in life. But people who are angry with God and feel let down in life are in the dangerous position of drifting deeper into rebellion. Blaming God and our circumstances is not the way our faces can be lifted up. What is the solution? (vs 6-7)

God likens sin to a dangerous beast waiting to pounce on a person as they come out the door. Many millennium's later the apostle Peter reminded Christians that “your adversary the devil prowls around like a roaring lion, seeking someone to devour.” (1 Peter 5:8) Peter's advice to Christians was that we must therefore “be sober-minded and watchful.” God's advice to Cain was: “If you do well, will you not be accepted?” The Hebrew for 'be accepted' can be translated as “will there not be a lifting up” of your face? The answer to fallen faces is to realize that we need to overcome sin rather than allow it to overcome us. Rather than being angry with God, we need to turn to Him for the help we need to be sober minded and watchful, and to do well rather than doing evil. Jesus is the one who can lift up our face and give us victory in this world (and life in the world to come) because God had regard for Him and the sacrifice He brought.