"The Problem of Evil" is a perennial question asked by those who are evaluating their beliefs.
It's a good question.
It does have a solution. See "True Reason" (2012), chapter 14, "The Problem of Evil and Reasonable Christian Responses" by John M. DePoe.
But the solution is a bit rubbish, because while it is perfectly logical, it is not anchored by any evidence, and it is exactly the same solution as for "The Problem of Good".
What? Not heard of "The Problem of Good"?
Let me show you.
In the beginning God created the heavens. 10 billion years later some of the heavens formed into the earth. God carefully manipulated quantum fluctuations to manipulate atoms, to manipulate proteins, to result in mutations that appeared to be totally random. He went to this effort to mess with the humans; the humans who did not yet exist. Then He manipulated quantum fluctuations to manipulate atoms to cause some of the life forms that resulted from those seemingly-random mutations to die before they could multiply; either by events that appeared to be accidental, or by predation by other life forms, or by cataclismic events, like asteroids, or massive volcanic eruptions, or global climate change. He hid His influence, again, just to mess with the humans. And mass extinctions make all the tedious physics feel worth it, for a while.
Worth it? Why?
Because when You have existed from before the beginning of time (whatever that means) and You are all-powerful, what else are You going to do? You're going to create, carefully, slowly, animals that can feel pain. And then You're going to inflict it. It's the only way to satisfy Your eons of maddening boredom.
Why not just create eternal torture?
That's not interesting. That's not fun.
Humans are interesting and fun. Humans are better than other animals. You can make animals suffer, but humans are different; humans are aware of their own suffering. Humans can consciously strive against their suffering, and inflict suffering on each other, in new and creative ways. That is several orders of magnitude more fun.
But You have to give the humans hope. Just an inkling, a teaser, that things could get better. That if they do this, or believe that, or worship You for Your infinite lovingkindness and mercy, then You will save them from the world You so carefully engineered. And in their desperate hope, they will forget that You engineered the world to be violent and dangerous before they existed, and You created them flawed so that they would screw it up even more.
Of course they would screw it up. That's the whole point. That's why You didn't create them strong enough to resist temptation. That's why You built them with millenia of complex and conflicting social behaviour. "Should I help my family by stealing from strangers?" "Should I kill out of vengeance?" "Should I kill to protect my family?" "Should I kill to protect society?" "Should I kill just to punish?" "The more kids I have the better chance my genes have to continue my legacy. My neighbour is rich, and he'll never know he's raising my children, and his wife is so hot. And she fancies me. And any way, he doesn't care about her the way I do." "That guy's weird. It's just not right. Being weird should be illegal. It's not what God wants. In fact, it should be punishable by death." "I just bought her a very expensive dinner. And I've wanted her for so long. She owes me."
Those little instinctive urges happen a million times every day. So You make some people strong enough to do the wise thing, and some dumb enough to go with their gut, and their gut tends to choose sex, food, sleep, and oxygen over generosity, selflessness and kindness.
Humans are more fun when you can make them fight. War brings out the best and the worst in humans. Some wars are easy; give them plenty, then give them drought. But the most fun are wars that recur century after century. And for that you need religion.
Here's the kicker. Reveal Yourself to individuals. Seldom more than one person at a time, and never to a whole society. Always make them take some poor crazy bastard's word for it. It shows how desperate they are.
And then, tell each guy something slightly different. Preferably conflicting in subtle ways.
Exclusivity is the best. Tell each guy that they are the only one who is completely correct, and everyone else is wrong; sometimes slightly wrong, sometimes completely wrong, but never more correct than them. That will totally screw with them. They'll argue endlessly.
But how do you bump an argument up to murder? Tell them about heaven and hell. Whoever is right will be rewarded with eternal happiness, and whoever is wrong will be tortured forever. You can't have more at stake than that. Now they will gladly die for fighting for what they think is right, and justifyably risk everything to fight against what they believe is wrong.
And now back to our original question: How do we explain the existence of good in a universe created by an evil God?
In order for His plan to work, for humans to be tormented to the maximum, they must have hope. Without hope, they will not try. And for hope you need islands of goodness in a sea of wretchedness. In order for the deep pits of sorrow so strong it feels like a physical disability, you need the occasional high peaks of joy.
But why is there so much good?
To contrast so much evil.
And if you think the good is outweighing the bad ... just you wait. You think you've seen evil? You haven't seen anything yet. Let the religiously fervent breed like vermin -- because that's what God told them, right? When the population size peaks, the fun really starts. Every germ finds a host body. Every bullets finds flesh. Every earthquake, every hurricane, every asteroid finds a city. For just a little while, finally, God won't be bored.
So you see, the solution to the Problem of Evil works even better as the solution to the Problem of Good.
So, John M. DePoe, do you have another solution to the Problem of Evil, or is that all you've got?