"The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him" (Ezek.18:20).
Those who teach original sin say that the sin of Adam was imputed to his son Abel and all of the descendants of Abraham:
"They (Adam & Eve) being the root of mankind, the guilt of this sin was imputed, and the same death in sin and corrupted nature conveyed to all their posterity, descending from them by original generation" [emphasis added] (The Westminster Confession of Faith, VI./3).
According to that the son, Abel, does indeed bear the iniquity of his father Adam. But the Lord will do no such thing. A person is not responsible for anyone's sins but his own.
How were all men made sinners by the offense of Adam? Simple. If he would have remained in innonence then "law" would not have come into the world and sin is not imputed when there is no law:
"...even as by one man sin entered into the world, and by sin death; and thus death passed upon all men, for that all have sinned: for until law sin was in the world; but sin is not put to account when there is no law" (Ro.5:12-13).
How did "law" cme into the world by Adam that lead to all men being sinners? When Adam ate of the "tree of the knowledge of good and evil" he had the knowledge of the law written in his heart and his "conscience" bore witness to that law. His very nature had changed. The Lord said:
"Behold,the man is become as one of us, to know good and evil" (Gen.3:22).
Adam now had a "conscience" of the law written in his heart. All of Adam's descendants would thereafter be born in Adam's likeness and image, also having a "conscience", or an inborn knowledge of God's law:
"And Adam lived an hundred and thirty years, and begat a son in his own likeness, and after his image; and called his name Seth" (Gen.5:3).
So Adam was responsible for death coming unto all men because he was responsible for bringing "law" unto all men. When all men after Adam sinned against the law written in their hearts they died spiritually--"and so death passed upon all men, for that all have sinned."