Well, they convinced me over in the welcome thread to participate, so here I am...
I'm glad you used the word illogic, because you are using a logical fallacy:
The flaw in this part of your argument is the assumption of premise two, namely that God does not want evil to exist.
There is no flaw in the premise and no flaw in the syllogism, you simply do not accept one of the premises, which is fine. I don't accept them either. It is just to show that an omnipotent, evil-hating God is illogical if evil exists. Very simple.
The flaw in this part of your argument is the assumption of premise two, namely that God does not want evil to exist.
Yes, this point has been made many times. God must want evil. But then, this calls into question the point about God being "good". It must be a very different definition of "good" than the one we normally use.
The only logical way you could come up with an idea like that is if you were deliberately trying to come up with a paradox. Because the first assumption one should make when presented with the other two premises (which you seem to be accepting) is the exact opposite.
The logical progression would be:
1. God Exists
2. God is omnipotent (All powerful)
3. God is good (edit)
4. Evil Exists
therefore
5. Evil has a Divine purpose. (Reason for existing.)
You too have set up a paradox. If evil has a divine purpose, the it's really good, not really evil, isn't it? So you see, in order for your syllogism to work, you must completely disregard the standard meanings of "good" and "evil", thus any logic that uses those terms is meaningless.
Leading us to the following:
Evil must exist for good to be knowable.
Easily demonstrated: Ask a friend to slap you in the face as hard as they can. Feels good when it stops doesn't it?
I would prefer that my friend did not slap me at all.
But again, you simply illustrate the impossibility of defining good and evil. If your friend were doing you a favor by slapping you (so that you could learn the difference between good and evil), then you could not say that slapping you was evil.
God is good. If there were no evil, then how would you know what good was? Good and evil can not exist independently of each other. To know God we must know evil...
One of the rules established by God was that man should have free will, the right to choose to serve God or not. Without the distinction between good and evil man has no choice.
I do not believe you can make a clear distinction between good and evil. There are simply "things which conform to your moral code" and "things that go against your moral code". But moral codes are not absolute things. They vary between people, and indeed they change during your life. For something to be truly evil, in my opinion, it must be always evil and serve no good purpose under any circumstances whatsoever (including teaching). I don't know of anything that fits this definition.
That is why it is pointless to discuss God in such absolute terms as "good" and "evil" because we simply have no idea what God wants. If He believes it is good to kill hundreds of thousands of people in a tsunami, then He must be using a very different meaning of "good" than we use, so why even bother to call Him "good"? He's simply unfathomable.
One of the rules established by God was that man should have free will, the right to choose to serve God or not. Without the distinction between good and evil man has no choice. We can debate about why this rule should exist, but to do so makes about as much sense as asking why gravity makes things fall down, rather than up (The concept of 'gravity' has been simplified for the purpose of analogy)
You can demonstrate that things fall down rather than up (or more correctly, "toward the center of gravity of the largest nearby mass"). You can
not demonstrate that a particular action is good or evil.