I understand perfectly well the Christian belief that Adam's nature was passed along to usYou're still not understanding why.
Adam's nature was passed along to us.
Adam's nature was separated from God, cutting him, and subsequently the rest of the human race, off from God.
"The damage" as you say, "passing from parent to child, down through the ages"
Do you understand, though, that the corrupt nature is inheritable because God consciously and purposefully chose that it be that way?
YHVH needlessly chose that the entire human race should suffer because of something that the 1st man did