Why is God just to punish Jesus for our sins when doing a similar thing would be so unjust for a human judge to do?

Very good question.

When Jesus died, he said, "Father, the hour has come. Glorify your Son and glorify yourself." And the Father came back and said, "I have glorified it [my name], and I will glorify it again."

The way to understand Jesus' substitutionary death under God's wrath is that he is doing it in such a way as to glorify or magnify the infinite worth of the glory of God.

God's glory has been trampled by people like us. Every time we prefer something to the glory of God, we demean the glory of God. And we do it every day.

Since his glory has been impugned and belittled, he has to exalt his glory by punishing sinners and saying, "My glory is infinitely valuable. If you trample my glory, you lose glory. And I restore my glory by your losing glory."

Jesus enters in and he is able to do what no human could do. This is why there is a difference. No human ever could do this in a court of law. He is so perfect and he suffers so much, and his motives are so Godward, that when he dies on the cross, what is manifest is, "Look how valuable the glory of God is!"

If a mom stepped forward in a courtroom and said, "Let me take my son's place. Let me take my son's place, please." We all know that would be unjust. She goes to the electric chair, and this son goes on to sin more.

The two differences are

1. She's not doing that to magnify the worth of the state—God. She's doing it to magnify the worth of her son, and that's not what's happening at the cross.
2. She's freeing the son, untransformed, to go into the world and sin some more.

And those are the very two things that are different about the death of Jesus.

1. Jesus dies not to magnify the sinner's worth, but to magnify God's worth.
2. And he dies and changes those who escape from hell. He doesn't just release more sin upon the world. He puts the Holy Spirit in our lives and begins to transform us into the image of Christ so that we bring more glory to the Father than if we had been left in our sin.