We inherit sin because it became the nature of humans. They separated themselves (humanity) from God at the moment of disobedience.
Who was created before A&E?
...Genesis 1...
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26]
And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
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27]
So God created man in his own image, in the image of God created he him; male and female created he them.
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28] And God blessed them, and
God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
….Followed in Genesis 2 by...
[7] And the LORD God
formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
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8] And the LORD God planted a garden eastward in Eden; and
there he put the man whom he had formed.
...So, some version of man and woman had already been created in God's image before this single man that was placed in the Garden of Eden….Then God makes a woman from the body of that man...
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18] And the LORD God said,
It is not good that the man should be alone; I will make him an help meet for him.
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19] And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof.
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20] And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him.
[21] And the LORD God caused a deep sleep to fall upon Adam and he slept: and he took one of his ribs, and closed up the flesh instead thereof;
[22] And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man.
[23] And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man.
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24] Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh.
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25] And they were both naked, the man and his wife, and were not ashamed.
…So, Adam and Eve and all their descendants were separate from the original set of man and woman that God created in His image...This is supported later on in Genesis 6, when it's revealed that angels(sons of God) were having sex with a separate group of people and creating giants...God didn't like this and decided to kill everybody in the flood except Noah and his family...
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4] There were giants in the earth in those days; and also after that, when
the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
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5] And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually.
[6] And it repented the LORD that he had made man on the earth, and it grieved him at his heart.
[7] And the LORD said, I will destroy man whom I have created from the face of the earth; both man, and beast, and the creeping thing, and the fowls of the air; for it repenteth me that I have made them.