Adam is a type of Christ, and as by Adam's sin natural death came on all who are his natural children, (for they all, like Adam, have sinned and suffer death as the consequence,) so by one man, Christ, spiritual life comes to all who are Christ's spiritual children.
This simply teaches that Adam as the head of a sinning race, who suffer death in consequence of his sin and their own, is an emblem or type of Christ, the head of a holy family, who by him receive spiritual life. Condemnation and natural death come from sinning, both to Adam and to all the children brought into being by him. Justification and spiritual life come from Christ to all whom he has caused to become his spiritual children.
For abundant proof that this was the interpretation of this passage, from the apostles to the time of Augustine, the author refers to Dr. E. Beecher's Conflict of Ages, book v., chapter 2.
Augustinian Interpretation.
The Augustinian interpretation is this: The sin of Adam caused a depraved nature and consequent spiritual death to all his descendants. So also the obedience [pg 231] and death of Christ have purchased or caused a holy nature and spiritual life to all who are regenerated.
Princeton Interpretation.
It has been shown that the Princeton theologians teach, that though all men did not sin in Adam, or sin at all, before they were born, yet God imputes Adam's sin to them, and regards and treats them as if they had committed it.
Their interpretation of this passage then is briefly this:
As by, or on account of, Adam's sin a condemning sentence came on all men, so by Christ's obedience a sentence of acquittal (i.e., justification) came on all who are regenerated.
According to these divines, verse 12 does not refer to a depraved nature nor to actual sin, but only to the fact that all suffer the penalty for Adam's sin through all time and eternity, unless they are regenerated. The Princeton school of divines are the most strongly Calvinistic in maintaining the total depravity of man and his entire inability to perform any truly virtuous act previous to regeneration.