The only coherent explanation I've read in any of the 'Passion' discussion goes thus: perfect justice means that people who do bad things must suffer. We are all so bad, even babies, that justice means we must suffer infinitely. God can't evade this fact, because it is a moral standard of perfection. All he could do was to redirect this inevitable suffering to another person. And he became a person to take on this punishment.
That explanation is intellectually coherent, in a formal sense. However I think it is quite false. 'Justice' is a way in which we restrict and direct primate aggression. Somebody hurts me, I feel a desire for revenge. Justice means that I should at least temper my aggression to what is proportional, and direct it at the right person.
What justice doesn't mean is that on some cosmic scale a person who has done wrong must be hurt. Justice limits aggression, it doesn't require it. Justice is a way of making the best of things in a society of grumpy social primates. When we care for each other, we have least recourse to justice. And we can only live at all because we step away from justice, towards reconciliation and mercy.