Penal Substitution Theory of the Atonement and the Justice of God

The centerpiece of Christian theology is the atonement. Various theories of the atonement have been put forth by theologians throughout Church History but the dominant one in evangelical circles is the Penal Substitution Theory. To emphasize this point, John MacArthur states

The doctrine Anselm articulated, known as the penal substitution theory of the atonement, has long been considered an essential aspect of all doctrine that is truly evangelical. Historically, all who have abandoned this view have led movements away from evangelicalism.

In simple terms, the penal substiutionary view states that Christ suffered the penalty for sin in man's place by dying on the cross. His death satisfies the holy wrath of God against sin and allows God to justly forgive sinners. This view seems at its root to be unjust. How can it be considered justice for an innocent party to suffer the penalty due a guilty party? This seems to run contrary to the basic idea of justice; yet we are told that it is precisely because of God's unswervable justice that the death of Christ was necessary.

Some will argue that Jesus died voluntarily, therefore it is just. That misses the point. I am talking about the justice of punishing the innocent for the guilty. A person could volunteer today to be executed in place of a death row inmate but that would not be allowed because it would not satisfy the basic essence of justice which is that the person who commits the crime is the one who must be punished.