This question is getting at the heart of what Christ's sacrifice truly means, and so answering it is a very specific and important endeavor.

The philosophical understanding here is as follows; there is a distinction between Christ's 'primary' and 'secondary' cause that is important to note, because if God as Christ truly took upon Himself the fullness of human punishment as a primary cause, Christ would have unjustly entered hell and faced eternal punishment, which would not be justified nor biblical. This however is not the primary cause of Christ; it is, rather, a secondary, or more precisely, consequential, effect. Christ's submitting to punishment follows as a consequence of Christ's primary effort of saving mankind, which includes Christ entering mankind by becoming man, and through His perfection that justifies men in the judgement of God, perfecting man if they have faith in His work.

St. Thomas Aquinas appeals to this view as well.

And in like fashion Christ's voluntary suffering was such a good act that, because of its being found in human nature, God was appeased for every offense of the human race with regard to those who are made one with the crucified Christ in the aforesaid manner

The idea is that the primary cause of Christ is one of perfection (God) saving imperfection (humanity), not of punishment. The phraseology of punishment follows consequentially from Christ's intention of saving mankind.

This now raises a needed elucidation of the distinction between the two types of moral punishment; namely satisfactory punishment (punishment that serves a restorative purpose, death being an example) and penal punishment (legalistic punishment that is enacted only to serve justice, an example being eternal torment in hell).

It is 'satisfactory punishment' that Christ took upon Himself on the cross and in death. Christ absolutely did not take upon Himself 'penal punishment', for such would indicate that Christ suffered due to some personal sin of His own. St. Thomas Aquinas considered satisfactory punishment to be of a penitent nature. Just as certain suffering can enhance faith, so certain acts of penance can enhance faith, and even more so since such acts are voluntary. For Christ to redeem fallen man, Christ had to be firstly perfect, so that while all men fell in the imperfection of Adam and Eve, all men can be considered perfect in Christ. But this perfection also had to account for the sins that have been committed by men. For if Christ merely became a perfect everlasting man there would be no hope for other men to perfectly relate themselves to such truth. In other words, Christ had to become a mediator for the human race, and not simply an example for them. The mediation needed for the human race was a perfect willingness to endure the potentially restorative punishment of death, in order that the original consequence of our sins might be born with patience and love, and consequently restored and resurrected. This perfect penance is witnessed in Christ willingly entering the satisfactory punishment of death, and His victory is confirmed in the Resurrection.

How is it just that Jesus, an innocent, would be punished for our sins?

Using only the yardstick of justice, it can seem puzzling that Jesus would willingly lay down his life.

John 10:15 As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep.

Matthew 26:53 Thinkest thou that I cannot now pray to my Father, and he shall presently give me more than twelve legions of angels?

Jesus was willing to pay for all the sin of the world not for justice, but for love.

John 15:13 Greater love hath no man than this, that a man lay down his life for his friends.

John 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.

Just

jəst/ 1. based on or behaving according to what is morally right and fair

Was it fair for Jesus to take on what we deserve so that we can be treated as He deserves? No.

However, is a voluntary act of self-renouncing love righteous? Certainly.

Before even the foundation of the world, the plan of salvation was already agreed upon by the Father, Son and Holy Spirit. (1 Peter 1:20)

It was the solution to sin - meant to uphold God's character as a just and merciful ruler.

Justice and judgment are the habitation of thy throne: mercy and truth shall go before thy face. (Psalms 89:14)

The question touches on a problem: the analogy between human justice and divine justice has its limits. Under human justice, each crime is associated with a proportional punishment. When the punishment (jail time, fine paid, restitution made, privileges in society revoked) is complete, then the crime has been paid for. We assume that people are capable of making such payments.

Under divine justice, the payment for sin - any sin - is death. (Genesis 3, Ezekiel 18.) The fate of all people is the same: "for all have sinned and fall short of the glory of God" (Romans 3:23). Having lost the only coin we have to pay God with - our soul - all of us are doomed to Hell unless someone else who has something of value will make a payment on our behalf. Since there are many billions of people in need of this same payment, a finite human life will not suffice. One human life can be offered in exchange for one other human life. Jesus Christ is human, but also divine. His life is infinite, so when he offers his life to pay for our sins, he is making an infinite payment, hence can save all people who accept his offer. As Hebrews 2:17 says: "For this reason he had to be made like them, fully human in every way, in order that he might become a merciful and faithful high priest in service to God, and that he might make atonement for the sins of the people."

So to make payment for people's sins, the payment must be a like payment (human life for human life, so the savior had to be human) and it had to be an infinite payment (the savior must be God). This does not yet answer the question of why Jesus' offering his life for others was just, but it establishes one important point: Jesus offering his life as a payment for our sins was the ONLY way that people could be spared eternal punishment in Hell. So if his offering his life was not just, then there was no just way to accomplish the salvation of humanity. Galatians 2:21 says, "I do not set aside the grace of God, for if righteousness could be gained through the law, Christ died for nothing!" Also, Matthew 26:39 says, "Going a little farther, he fell with his face to the ground and prayed, 'My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will.'” If Jesus, who is God, asks his loving and compassionate Father, who is God, for another way to save the world beside going to the cross, and he is not told, "Yes, there is another way - do this instead" then there certainly was no other way.

So Jesus' life is a like offering (human life for human life), proportionate, and necessary. Also, since Jesus never sinned, his offering is unblemished, else God would not have accepted it. Now to talk about justice. When asked what the most important commandment was, Jesus answered, "'Love the Lord your God with all your heart and with all your soul and with all your strength and with all your mind'; and, 'Love your neighbor as yourself.'" (Luke 10:27) That summed up the whole law.

Jesus made an important statement about love: "Greater love has no one than this: to lay down one's life for one's friends." (John 15:13) So if the law (justice) is to love, and the highest form of love is to give your life for the one's you love, then Jesus' sacrifice was just.

This is certainly a challenging question. I'll rely on the writings of two prominent reformed theologians, Louis Berkhof and Charles Hodge, who are strong supporters of this doctrine. It's important to note, for reasons that will become clear, that they defend their position in the face of arguments made by opponents who believe in a just God. Those who reject the existence of a just God due to the problem of evil, for example, are not in view.

Briefly, the arguments are 1) there are certain circumstances in which human judges can transfer criminal punishment, and those circumstances apply to Jesus, 2) the testimony of the Bible demonstrates that it is just, and 3) it is presumptuous to put one's own sense of justice over that of God's.

Human analogies

Berkhof begins his treatment by recognizing that "[t]here is undoubtedly a real difficulty here," particularly because the idea of a just God pouring out judgement on an innocent party rather than the guilty party "seems to be contrary to all human analogy." Along these lines Berkhof does suggest a few examples from the secular world, such as substitution in the case of mandatory military service.

Berkhof's main argument here, however, is that even in the case of criminal law, there are circumstances in which substitution is legitimate. He quotes Amour's Atonement and Law:

"[L]aw, as understood and administered by men in all lands, provides that the penalty may be met by a substitute, in all cases in which the penalty prescribed is such that a substitute may meet it consistently with the obligations he is already under."

Berkhof lays out some of the criteria under which a human judge might permit substitution: (1) the guilty party is not able to bear the punishment, (2) the substitution does not infringe on the rights of any innocent third parties, (3) the substitute is not already indebted to justice, and (4) the guilty party retains consciousness of guilt. Saying that "[i]t is perfectly evident that the law does recognize the principle of substitution," he admits difficulty but defends the position, saying,

In view of all this it will be understood that the transfer of penal debt is well-nigh, if not entirely, impossible among men. But in the case of Christ, which is altogether unique, because in it a situation obtained which has no parallel, all the conditions named were met. There was no injustice of any kind.

He continues:

[T]he fact that it is impossible to find men who meet these requirements, is no proof that Jesus Christ could not meet them. In fact, He could and did, and was therefore an acceptable substitute.

Testimony of the Bible

With respect to the Bible's teachings, Charles Hodge succinctly defends the doctrine from attack as follows:

If the Bible teaches that the innocent may bear the guilt of the actual transgressor; that He may endure the penalty incurred in his place, then it is in vain to say that this cannot be done.

This argument will fall flat to any who do not accept the Bible as divinely inspired, but Hodge's point is that the teachings of Scripture overwhelming support this doctrine, leaving "us no alternative but to receive them as the truths of God, or to reject the Bible as his word."

As a side note, some of the points along these lines are the expiatory and substitutionary nature of Old Testament sacrifices (Leviticus 1:4, 16:20-22, and 17:11), the teaching of our sins being laid upon Christ (Isaiah 53:6, 53:12; Galatians 3:13; Hebrews 9:28; 1 Peter 2:24), and that the prepositions used in these and other passage must mean "instead of," not "on behalf of," upon thorough evaluation of all uses of these words in the New Testament. (see Berkhof for more on this)

God is Justice

Addressing those who find the last argument unconvincing, Hodge calls on his opponents to consider:

Rejecting the Bible does not help the matter. We cannot reject the facts of providence. Where is the propriety of saying that the innocent cannot justly suffer for the guilty, when we see that they actually do thus suffer continually, and everywhere since the world began? [...] In teaching the doctrine of legal substitution, [...] the Bible asserts and assumes no moral principle which does not underlie all the providential dealings of God with individuals or with nations.

The point, Hodge says, is that men foolishly attempt to judge God for his supposed injustice, instead of recognizing that God defines what justice is. "Men," he says, "constantly deceive themselves by postulating as moral axioms what are nothing more than the forms in which their feelings or peculiar opinions find expression." If all these opinions are left unchecked,

[t]here would be no end of controversy, and no security for any truth whatever, if the strong personal convictions of individual minds be allowed to determine what is, or what is not true, what the Bible may, and what it may not, be allowed to teach.

He summarizes:

[T]here is nothing in the nature of things, nothing in the moral nature of man, nothing in the nature of God as revealed either in his providence or in his word, which forbids the idea that this obligation may on adequate grounds be transferred from one to another, or assumed by one in the place of others. (532)

Berkhof addresses these objections similarly, and also emphasizes that Christ's substitutionary work was voluntary, part of "a solemn agreement between the three persons in the Godhead." Furthermore, he argues that those who deny substitutionary atonement are forced to defend God's injustice for unnecessarily subjecting his Son to suffering and death.

Closing points

Obviously, as mentioned at the beginning, the arguments made by these two theologians will not be found particularly satisfactory to those who object to the existence of God based on the problem of evil. Without the common ground of belief in a just God who reveals himself in the Bible, arguments to defend the justice of penal substitution will be ignored for the same reason as arguments to defend God's justice in allowing pain and suffering in the world.

However, for those who believe that a just God exists, Berkhof and Hodge argue that human analogies for penal substitutionary atonement are available, that rejection of the doctrine requires rejection of the clear teaching of the Bible, and that our understanding of the nature of justice must be informed by God's revelation, not merely our intuitions.

References:

• Berkhof, Systematic Theology, 3.3.4
• Hodge, Systematic Theology, 2.3.7.7