In the evidential problem of evil, the argument starts from: perhaps it is possible for God and Evil to co-exist, but it is not possible for there to be both. If U3 evil exists then it indicates O3 god doesn't exist. The argument has several propositions: An O3 God would eliminate all U3 evil. There appear to be instances of U3 evil. The best explanation of this evidence is that an O3 God doesn't exist. If H is the best explanation of E, then H is probably true. So, it's likely that an 03 God doesn't exist. Is this argument compelling? A. Yes, the argument is cogent and provides a theist with a good reason to doubt that God exists. B. No, the argument isn't abductively strong.C. No, the argument is abductively strong, but one or more of the premises are false (or at least not plausible to a theist).D. No, the argument isn't abductively strong and one or more of the premises are false. Which one is correct and why?

In the universe God is not the only one. He created evil. He casts his own son Lucifer to Hell. There must be a balance between Divine and Evil. Not to forget that His son was a former angel. If there was only God , who would know what life would be without evil things. If there would be evil, it would be total caos as no one would fight for good.

I think that one of the basic premises—that God would eliminate all evil—is flawed.
This requires several leaps which are not addressed in your supports. First, it requires a knowledge of God's intent, which is impossible. All gods throughout history have been acknowledged to have thoughts higher than mankind, and humans have accepted that they cannot know the will of God as they exist in physical separation. To therefore assert from a human standpoint that God would definitely make any decision is an unsupported assertion.
The very definition of "evil" also defines some moral code not addressed in your arguments. If humans accept certain behavior as "evil," who has defined the ultimate moral code? What is evil? And for whom? When were these moral laws established? For what purpose? This is also not evident in the support that follows.
What about the argument that if a world without evil existed God would then be forced to then create humans as puppets with no free will or choice? If God's hand sweeps down to remove evil from the world, He therefore also creates humans who are forced to behave in a certain way. Perhaps it is the free choice inherent in this creation that allows for humans themselves to create both beauty and disaster: both love and suffering. This is also missing from your argument.
And finally, an argument not addressed is that God hasn't eliminated all evil yet. Perhaps this is an event yet to come.
I think the argument falls flat because of too many unsupported leaps made in the initial assertion. (The H and E references didn't come through in your question, but I would say that 1 is weak and then 3 therefore isn't a clear support as there are other pieces of evidence that would disqualify the "best explanation.")