But if God is sovereign, then his rules are not arbitrary
How do you figure? Even if he rules absolutely and can bend the universe at will, rules like 'don't wear two types of cloth together' are still bizarre and arbitrary.
If you remove God's sovereignty, sure.
The problem of Evil was one that Christians could never answer.
Christians say:
1- God Exists.
2- God knows everything: Everything that was, is and what will be.
3- God can do everything: There are no limits to his power.
4- God is all loving: he loves all of his creations and wishes no harm upon them.
The facts
1- There is and was crime in the world.
The implications are:
1- God knew who was going to commit crimes before they even existed.
2- God could have prevented them, but did not try.
With all of these premises, we must arrive to at least one of these conclusions:
1- God is not Omnipotent: He could not prevent crime.
2- God is not Omniscient: He did not know of all the crimes.
3- God is not Omnibenevolent: He would send his creations to hell for a crime, rather than preventing the crime.
4- God is not Real: Crimes happen naturally.
My question
Which one of these options do you choose? You can't logically deny them all.
You are making the mistake of applying your own morality to God, this is the flaw with your third conclusion. When you come to understand that God is not human and bound by human perceptions of what is right and wrong, you will understand that he can be omnipotent, omniscient, omnibenevolent, and still allow for bad things to happen in the world. Just as a clay vessel doesn't have the moral authority to complain about how the potter created it, we don't have the moral authority to say that God's plan for the universe is flawed. Even still, the comparison between a pot and a potter doesn't even come close to the disparity between man and God.
I think that you are correct on all your points, but why would this mean that God is not just? Has he not given us a way out of the situation you described?
A way out? That would imply the existence of free will, which you yourself have admitted we do not have. In your narrative, we are nothing but puppets, our entire lives pre-ordained before we are even born.
But we have the illusion of free will, which as far as you and I are concerned is sufficient. Though God knew everything I would ever do and thus preordained that it would happen by simply setting the universe into motion, it does not in any way excuse me from the sins I commit, since I myself do not know everything that the future holds. Likewise, you must assume that you are one of the elect. Rejecting God on the grounds that "God already knew I wouldn't accept him" doesn't justify your decision.
I don't buy that. In the Christian view, sin is a choice: a choice to act selfishly or against God. If you have no true free will, you cannot make a choice. How can you go against God's plan if -by the pre-ordination of every second of your existence- every thought, action and breath you take is God's plan?
Also, what I assume is meaningless if my entire life is preordained. Either I will do the "right" things and go to Heaven, or I will do the "wrong" things and go to Hell, these paths were set in stone aeons before I existed. In the absence of free will, nothing I think or assume matters (if thought can truly be called thought without a mind capable of decisions).
I didn't think you bought any of this. We cannot possibly go against God's plan, but simply because my actions are the sum total of all my experiences, my biology, and my impulses and God in his infinite wisdom knows precisely what choice I will make, how does that justify my decision to commit a sin, such as murdering somebody?
Your life does have purpose for one reason, that God of the universe that preordained your existence said it does, even if your purpose goes no further than commiting your life to serving him.