I have an answer but whenever i trot it out seems people have an hard time getting it, and that's because the answer is metaphysical and metaphysics have been completely banished from western thought ever since the Renaissance.
See, the question itself already shows that you are looking at the problem from the wrong angle, as most people do as they speak of the existence of "evil". The truth is that if you really think about the implications of God's nature as an omnipotent, eternal "absolute" being, there's actually no "logical" reason for anything to exist at all, let alone evil.
Let me explain. The traditional understanding of God is that he is an all powerful, eternal "something" that exists outside both space and time and is the basis for all being. Not just any being, but the source of being itself. A lot of modern Christians have a completely anthropomorphic view of God, an heretical understanding of God from the point of view of traditional Christianity as well as many other religions, and generally speaking what atheists are arguing against is this anthropomorphic strawman (the bearded dude in the sky argument).
With all this said, think about it for a second. If God is eternal and absolute, that means that God is basically perfect existence, who exists in an unchanging perfect "present". So really, forget about evil, why does such an entity need to create anything at all? What for? He is already perfect as it is. He cannot possibly have a "want" for companionship, or the necessity to play with inferior entities.
There's no reason whatsoever such a powerful being would have to create anything whatsoever UNLESS we posit that he creates because he has no choice, but understanding that requires a true metaphysical understanding of his nature and the process of creation, which is actually an emanation:
The logic of this argument is as follow. If God is Absolute, than it means he must be both Infinite and Perfect (hence, Good, in the supreme sense). But infinity implies everything, even that which is finite and imperfect, except the finite and imperfect cannot exist at the same level as the infinite and the perfect, by definition, therefore, those possibilities must play out somewhere else, somewhere that is ontologically "lower" than the reality God himself inhabits, hence, the existence of creation, where the infinity of God exhausts itself in an infinite play of forms, cycles and so on.
Basically, creation exists because of what God IS, and since God cannot not be what he is, he cannot not will creation, and since creation is not God, he cannot prevent evil, for if creation was perfect it would just BE God and then only God would exist as absolute and absolute, infinite and infinite don't add to each other, they would just overlap.
At this point you can ask, but doesn't that contradict the notion that God is omnipotent, if he does not have the power not to be what he is? No, because that would be like saying that the infinite cannot be truly infinite until it has the ability to be finite, which is the kind of argument the Epicureans are basically making, because they don't understand the difference between absolute and relative, or between Atma and Maya as the Hindu would say. Basically, God is not actually above paradox, and it makes no sense to ask whether an all-power being has the "power" not to be all-powerful. It's the kind of argument that makes sense "logically" but not metaphysically.
I don't know whether you understand this, most people seem unable to do so, but the gist essentially is that creation is just part of the nature of God, and that creation is what it is because it cannot be God, therefore, creation has to be what it is whether you like it or not and the question for why evil exists is meaningless, because it's not really the question that truly matters. What matters is how we can return to the source of everything that is, where we can experience neither evil nor suffering, and the answer to that is that God himself showed us the way, by means of religion. In this context, "suffering" in this earth can either be a prelude towards damnation or a wake up call from God to force us to return to him. Buddhists believe that suffering is good because it allows us to burn negative Karma. And the Muslims say that God's "justice" has to assert itself before his mercy can be made manifest, but that ultimately his mercy is greater than his justice. All those things point to the fact that suffering in this life is not always a bad thing, once you understand that what matters is what happens to us in the next world, and that ultimately good will always triumph in the end because while evil can only exist within this lower relative space we call creation, good is an absolute and eternal quality of God himself. So nothing is ever actually "lost", which means despair has no place in a metaphysical conception of God and our place in the cosmos.
