From What is the Gospel, by Greg Gilbert:
The Heart of the Gospel
Sadly, this doctrine of substitution is probably the one part of the Christian gospel that the world hates most. People are simply disgusted at an idea of Jesus being punished for someone else’s sin. More than one author has called it “divine child abuse”. And yet to toss substitutionary atonement aside is to cut out the heart of the gospel. To be sure, there are many pictures in Scripture of what Christ accomplished with his death: example, reconciliation, and victory, to name three. But underneath them all is the reality to which all the other images point—penal substitution. You simply cannot leave it out, or even downplay it in favor of other images, or else you litter the landscape of Scripture with unanswered questions.
Why the sacrifices? What did the shedding of blood accomplish? How can God have mercy on sinner without destroying justice? What can it mean that God forgives iniquity and transgression and sin, and yet by no means clears the guilty (Ex. 34.7)? How can a righteous and holy God justify the ungodly (Rom 4:5)?
The answer to all these questions is found at the cross of Calvary, Jesus’ subsititionary death for his people. A righteous and holy God can justify the ungodly because in Jesus’ death, mercy and justice were perfectly reconciled. The curse was righteously executed, and we were mercifully saved.
(HT: Marco Gonzalez)