How does the idea of Christ suffering and dying on our behalf, taking our place and becoming a sin for us, correspond with our perception of justice. Most would say that someone being punished on behalf of another is not just at all. Leon Morris addresses this issue in this excerpt from The Apostolic Preaching of the Cross.
It is objected to this interpretation that the bearing of penalty by one in the place of another is not really just, so that when Christ suffers for us it is not a matter of fulfilling legal requirements. There is some force in this objection, and there would be more if we were dealing with a human law. But the fact is that we are not. The law in question is the law of God's holy nature, and that nature is merciful as well as just. Thus God's justice, while it is not capricious but works by the method of law, is a justice which finds a large place for mercy and is not hard, bare, and legalistic. At any rate, whether our legal categories can find a place for mercy or not, those of the Bible can and do ... neither justice nor mercy must be whittled down; but neither must they be separated.
(Morris, Leon. The Apostolic Preaching of the Cross. Grand Rapids: Eerdmans, 1965. Print. 280)