I think the key to this lies in scripture.
Gen 2:17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.
here we find the command to not eat of this tree. The disobedience to this command would result in death.
As we know they did eat of the tree. why?
Gen 3:4 And the serpent said unto the woman, Ye shall not surely die:
serpent/Devil Rev 12:9, lies to Eve.
Joh 8:44 Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.
So the Devil lies to Eve and then makes it look like God's real reason for stopping them eating it is because they will become like Him.
Gen 3:5 For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.
What Did Eve then do?
Gen 3:6 And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her; and he did eat.
She saw the food of the tree and found it pleasant and desirable for wisdom and then ate. what did she do?
Exo 20:17 Thou shalt not covet...
She broke the law of love.
one might even say this is theft being that she was told not to eat of it. but anyway. she sinned in eating the food of the tree.
we know they sinned why?
Rom 5:14 Nevertheless death reigned from Adam to Moses, even over them that had not sinned after the similitude of Adam's transgression, who is the figure of him that was to come.
Adam transgressed or sinned. and from this death passed to all men why?
Rom 5:12 Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
Rom 3:23 For all have sinned, and come short of the glory of God;
because all have sinned.
so the word is clear that it is not Adams sin that we are punished for but rather our own. however through Adams sin, sin entered the world. why?
The answer lies in the solution.
Rom 5:15 But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many.
Rom 5:19 For as by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous.
by seeing how God saved us through Jesus and thus brings us into obedience we will understand how by Adam many were brought into disobedience.
skipping a whole lot a scriptures and assuming everyone knows how we are made righteous by Christ through the power of the Holy Spirit or in short Jesus becomes our Lord and master. meaning the Satan was our Master beforehand.
Rom 6:16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
Joh 8:34 Jesus answered them, Verily, verily, I say unto you, Whosoever committeth sin is the servant of sin.
Joh 8:35 And the servant abideth not in the house for ever: but the Son abideth ever.
Joh 8:36 If the Son therefore shall make you free, ye shall be free indeed.
Jesus frees us from being slaves to sin. Satan is the master of sin.
Going back to the fall we see that Eve and Adam chose to obey who?
God says don't eat, will die.
Satan says, eat, wont die.
When Adam and Eve chose to obey Satan they became slaves to Him and thus the human race was born into slavery.
Rom 6:17 But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you.
Rom 6:18 Being then made free from sin, ye became the servants of righteousness.
Rom 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
so in short, Adam and Eve disobeyed God and served Satan and thus became slaves to the one who they obeyed. This caused all mankind to be born under the rule of Satan and thus bound by sin. Jesus came to save us and offer a way for us to receive God as our master again through His blood.
Rom 5:10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life.
We have been reconciled to God. no more slaves to Satan.