This is a post designed to answer deeper theological questions. I've asked Facebook friends to post questions for discussion. I'll make a humble attempt to explore these questions from a biblical perspective.
Q: I've never understood the "how" behind Jesus' substitutionary sacrifice. How does his righteousness get transferred to us and our sin to Him? Why is a substitution acceptable to God, even in the Mosaic law? --Lewis Crow
A: Lewis, this question of substitution has been on my mind as well. In the Law, God allowed a penal [legal] substitute for human sin. Declaring that the penalty of sin is death [Romans 3:23], He chose to allow one to die for another. Before Christ, an unblemished lamb [aka "scapegoat"] could serve as the substitute for a penitent sinner. In the New Testament, Jesus becomes the perfect Lamb of God who takes away the sins of the world [John 1:29].
This idea of substitution is known as "imputation." Three imputations are found in the Bible and in our human experience. First, Adam's sin is imputed to us. Sin entered the world through this one representative man and was laid upon everyone who would be descended from him [see Romans 5:12ff].
Second, our sin is imputed to Christ. While some cry "foul!" because we are held responsible for something Adam started, they don't mind letting Jesus bear the punishment for something we did. Isaiah writes that "God laid on Him the iniquity of us all" [53:6].
The last imputation is Christ's righteousness given to us. Paul writes, "God made him who had no sin to be sin for us, so that in him we might become the righteousness of God" [2 Corinthians 5:21]. As we trust in Jesus Christ, His righteousness replaces our sin. In this great exchange, we become acceptable to God.
These three imputations are mysterious principles of creation ordained by God. I consider them an expression of His grace--making it possible for sin to be justly condemned and sinners to be reconciled to God through the substitutionary work of a perfect God-man.
I hope this helps.