You're absolutely right, but keep in mind that there is more than one version of the Adam & Eve story and nobody knows for sure which one we should stick with.
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The "mystery" of the Serpent's Seed.....
In the garden of God, the Serpent walked upright, talked to Eve, and eventually beguiled her into disbelieving God's word and believing the devil's lie. The true meaning of the word sin is "unbelief", This Serpent however was merely an animal, and therefore could be possessed and used by the devil, for it did not have a soul like a Man. The Serpent was the closest member of the animal species to Man. Adam was created in the image of God, an attribute of God's own genes, a Son of God. And like a son grows up to reflect the image of his father, Adam was to reflect God's image , to manifest God in this physical realm. He was created the first of a new species, higher in power and authority than the angels," The Sons of God". Eve was not in the original creation, but was taken from Adam, a by-product, this is why she could be deceived. Lucifer had stated "he desired a kingdom more glorious than Michael's" , and said "I will ascend up and set as God and be worshipped as God". The scriptures say he deceived one-third of the angels in heaven, and when he spoke through the serpent to deceive Eve he was trying to carry out his plans to destroy God's future kingdom and create his own "Satan's Eden ", where he sits as God, and is worshipped as God, by all the peoples of the earth. Science, education, and modern civilization are all a part of his plan to get people to lean on their own understanding, instead of faith in God, who is the Word (1 john 1:1-14 ).
The bible says "God himself came down in the cool of the evening, and talked with Adam". As he listened to the words God spoke he was partaking (eating ) of the Tree of Life, who is God (In the book of Proverbs it says, "the words of a righteous man are as the fruits of the tree of life")The tree of the knowledge of good and evil , was the serpent , which they were commanded not to eat of least they die. ( a mixed tree containing the truth mixed with lies) The best lie is the one that contains 99% of the truth, and only 1% lie. The Serpent said to Eve, "surely you shall not die, but your eyes shall be opened and you shall be like gods". Adam was created by the spoken Word. Satan can not create something from nothing, he can only pervert something God has already created, so he used the serpent to seduce Eve and thereby create a hybrid race. It's been documented many times that a woman can have sex with two different men within a 24 hour period and conceive by both of them ,giving birth to twins, both of different fathers. The scriptures say "Cain was of his father the wicked one", And after being with the serpent, Eve went to show Adam this that she'd learned, the bible says" Adam knew his wife Eve, and she bore him a son, Cain, and then bare his brother Abel. So there are two sons representing two separate races, The Sons of God, and the Sons of Men.
Abel, being a true Son of God, received revelation from God about what had happened in the garden , that it had been blood (not an apple or something) that had caused the fall and had driven them out, and it would take blood, the blood of an innocent one, to bring them back to an unfallen state. Since the whole human race had fell into sin, he saw it would take a kinsman redeemer (Jesus Christ), God coming down as a man to die for our sins, releasing His Holy Spirit to come back upon humanity as a tutor and guide them back into all truth .
God revealed to him that a lamb would be accepted in the place of the real propitiation for our sins as a type or shadow of the real until it came.
In the new testament it says " they who are led by the spirit of God, these are called the Sons of God". Cain received no such revelation, being of the serpent's seed, and offered to God a selection of the grains of the field , which were the fruits of his own labors, and his offering was rejected. After Abel was killed, Adam had another son through Eve and his name was Seth. Through Seth's lineage God's line was restored.
