>I understand that Christianity often wants to redefine these words in order to make them compatible... But they are indeed mutually exclusive per the English language definitions of those words.
This is just false, but if you want to think that way, go ahead. But I would really appreciate it if you would give me your definition of justice and mercy.
>That doesn't make any sense. If person a commits a crime and then person b gets punished for it, no person in their right mind would say justice had been done. That's not how justice works.
I don't see how it doesn't make sense. There are actual systems today that have this exact justice system. William Lane Craig has written a book on the atonement (The atonement and the Death of Christ) where he mentions this very thing. I get that punishing someone for a crime that they didn't commit may sound odd, but if they want to take the punishment for someone else, they can do that if they so will.
>I meant the idea that he is bound by justice and that he cannot change it. He is required to comply with some set of justice. The fact that it is his will that justice should be done means that he's not merciful by deifnition.
Well, when you say 'bound by justice' it sounds like that is a bad thing. But justice is a great thing, and God is a maximally great being, so if he is unjust, then he is not maximally great. And it is not that he is required, but rather it's in his very nature to be just. It's not like God is thinking "I wish I could do something different" since justice is a part of his nature, he naturally does acts of justice. You say "The fact that it is his will that justice should be done means that he's not merciful by deifnition." How does this follow? It's his will to be just, and merciful. And he can accomplish bother by Christ's death on the Cross. Justice was satisfied, thereby making mercy possible.
>Imagine making a demand of an omnipotent creator and that omnipotent creator being required to comply... Who exactly is forcing God to punish? Who or what has the authority to tell God he must punish?
I think you have a misunderstanding of What Christians mean by omnipotence. We do not mean the ability to do anything. We mean the ability to do whatever is logically possible. And it's not that God is being forced by some external factor, but rather it is God's very nature to be just, Justice is a good quality, not a bad one. And God is a maximally great being, must be just. And it is logically impossible for God to go against his own nature.
>An omnipotent God doesn't desire anything they don't have. If God desired all to be saved... All would be saved. If God desires all to be saved and some are not saved, he's not omnipotent.
Again, this is a misunderstanding of what omnipotence means. It is logically impossible for God to make free creatures do something. So, it may be God's desire that all be saved, but all can't be saved because humans have free will to choose otherwise.
>Parents who "punish" their kids eternally are horrible parents. Parents who punish their kid with a punishment that is worse than the crime are horrific parents. God is not a good model of a good parent.
I do agree with you that "Parents who punish their kid with a punishment that is worse than the crime are horrific parents. " And God does the same thing, he doesn't punish people for more than what they deserve. But you may say "But isn't hell eternal?" There are different views out there, and there are many Christians who hold to annihilationism, the view that people will serve their punishment, then be annihilated. And, even if you believe hell is eternal as I do, there are still ways to reconcile such a view. For example, who's to say that people stop sinning in hell? If people continue to sin in hell, then their punishment continues to get extended. But no matter what your view is on hell, God, if he actually does exist, has to be fair so it would be impossible for God to punish someone that is not equal to crimes they have committed.