Again, sin indeed does have consequences upon succeeding generations, but those consequences are NOT, in and of themselves, sin or sinful.
What sin did Adam commit? He rebelled against God. What consequences did that have for the human race? Let's look at it.
First, notice that Adam was made in the image and likeness of God.
Genesis 1:27 So God created man in his own image, in the image of God created he him; male and female created he them.
--Then Adam disobeyed God, and faced the consequences of his sin. What were they?
Genesis 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.
--Adam would die--both spiritually and physically.
He died spiritually right away. The first thing he did was to hide from God. They were aware of their nakedness, ashamed, and tried to hide.
They became afraid of God. Sin had separated them from God. Death is separation. They were spiritually separated; spiritually dead.
Adam lived 930 years and then died--physically.
What else happened?
Genesis 5:3 And Adam lived an hundred and thirty years, and
begat a son in his own likeness, after his image; and called his name Seth:
--Remember that Adam was made in the image and likeness of God.
But what happened here? Seth was born but was not made in the image and likeness of God. He was made in the likeness of Adam. The image and likeness of God had been marred. It would be no longer. Seth now had inherited Adam's likeness which was marred by sin. This we call a sin nature, a nature that was marred by the fall or the curse resulting from the fall. This consequence would be handed down from Adam to each successive generation, to each and every person, because of Adam's sin. He was the federal head of the human race, and from henceforth all would be made in his image, not God's. This is where that inherent sin nature comes from.
--A child is not born in innocence. It is born with a sin nature.
Now the unsaved are known as:
children of this world (Luke 16:18)
children of the flesh (Romans 9:8)
children of the devil (John 8:44)
children of disobedience (Ephesians 2:2)
children of wrath (Ephesians 2:3)
Cursed children (2Peter 2:14)
They have never been known by God (Matthew 7:23)
They are aliens and strangers (Ephesians 2:12)
They are foreigners (Ephesians 2:19)
They are servants of sin (John 8:34)
They are servants of corruption (2Peter 2:19)
They are without Christ, without hope, and without God (Ephesians 2:12)
They are dead in sin (Ephesians 2:5)
They are condemned to death (John 3:18)
Even the fact that the Lord says: I never knew you. Never means never--not even as a fetus. The unsaved person has a sin nature. Sin condemns a person. It causes a person by nature to reject Christ. Though we are accountable ultimately for our own sin; our sin nature doesn't help any.