-Genesis 4: 6-7
If we are born under the dominion of satan, in original sin, and unable to perform any good works without the supernatural intervention of grace, why does God specifically tell Cain that he has the power to avoid sin (ie "rule over it)?
Cain would surely have been born in original sin right? Surely he would have been under the domain of satan, as the RCC alleges all human beings are from birth, right? So, why does God tell him that he can become “ruler” over sin?
'And the Lord said to Cain, "Why are you annoyed, and why has your countenance fallen? Is it not so that if you improve, it will be forgiven you? If you do not improve, however, at the entrance, sin is lying, and to you is its longing, but you can rule over it."’
If we are able to perform any good work without the aid of supernatural grace, why did God intervene to save Cain from spiritual death? Why was it that God did not accept Cain’s sacrificial offerings (good works)?. How was it that Cain harboured jealousy and anger towards his brother Abel and was vexed with God for having rejected his “good works” (sacrificial offerings) without the stain of original sin on his soul? How was it that Cain had the ability to master sin but eventually murdered his brother?

The passage that you cited must be read in context with the entire story of Cain and Abel.
This biblical narrative actually supports the Catholic dogma of original sin and our dependence on God for the actual graces we need to perform supernatural deeds necessary for salvation. Efficacious (cooperative) grace is the actual grace to which human consent is freely given so that it produces the intended supernatural effect. Substantially this grace is the Divine persuasion and influence which is communicated to help us overcome our disordered passions and desires that lead to vice. Using Catholic terminology we can say that God offered Cain the actual graces of humility, repentance, and conversion that would allow him to transcend his natural inclinations and rid him of his disordered disposition – thereby sanctifying his soul. By the unmerited operation of God’s sufficient (operative) grace, Cain had the ability to humble himself, acknowledge his guilt and feel sincerely sorry for it, and convert from his sinful way. Unfortunately, however, he freely resisted God’s intervention and chose not to co-operate with Him by allowing himself to be persuaded by God.
Cain refused to accept the divine truth which God wanted him to understand so that his sacrificial offerings would be pleasing and acceptable; that is he had no reason to be jealous of his brother Abel and angry with him, and vexed with God for having rejected his offerings while accepting those of Abel. The real reason why God rejected his offerings was because Cain would not acknowledge his guilt before God for all his sins. Cain’s natural ability to reason without the light of faith could not have helped him and save his soul from spiritual death, for this faculty of ours does not essentially belong to the supernatural order of our being. God’s intervention and influence was absolutely required.
In any event, Cain’s innate dark passions, which he allowed free reign in his hardness of heart, took predominance over the Divine influence. The truth is, that because of his ego, he thought more about himself than he did about God and Abel. In his pride and inordinate self-love, all he could see was that he was being unjustly treated. He felt that his offering sacrifices to God should in and of themselves justify him and make God indebted to him despite the hatred and jealousy he felt for his brother while presenting his offerings… Cain failed to see how his own faithlessness rendered his sacrifices unworthy. So only by divine intervention could he understand why God had rejected his offerings. He couldn’t see for himself how necessary it was for him to acknowledge his guilt before God so as to make his offerings acceptable and pleasing to Him. God honored Cain’s free will when He mercifully aided him in his spiritual conflict with the power of darkness. And God permitted Cain’s blindness to the truth to overwhelm him. God abandoned Cain to himself as he chose not to cooperate with Him under His benign influence and left him under the dominion of the devil. Without God’s intervening grace there to assist him in his slavery to sin, Cain eventually succumbed to Satan’s temptation and murdered his brother Abel.
O Lord, open my lips,
and my mouth will declare your praise.
For you have no delight in sacrifice;
if I were to give a burnt offering, you would not be pleased.
The sacrifice acceptable to God[d] is a broken spirit;
a broken and contrite heart, O God, you will not despise.
Psalm 51, 15-17
“Therefore if you are presenting your offering at the altar, and there remember that your brother has something against you, leave your offering there before the altar and go; first be reconciled to your brother, and then come and present your offering.”
Matthew 5, 23-24
The need to humble ourselves, admit our guilt, and be reconciled with God and our neighbour isn’t something we can grasp by the natural light of reason uninformed by the light of faith. Nor can we by nature alone act humbly and put the interests of others above our own interests without the help of God’s grace. These are supernatural acts of salvific value.
"For out of the heart come evil thoughts—
murder, adultery, sexual immorality, theft, false testimony, slander. These are what defile a person; but eating with unwashed hands does not defile them.”
Matthew 15, 19-20
Guilt by association -----> actual guilt!
PAX
:heaven: