The Problem of Evil (also known as the Inconsistent Triad). In very simple terms there cannot exist evil and a benevolent, omnipotent God.
However, the problem may also be expressed, as evil exists because:
1) God can do nothing to prevent it occurring.
2) God is not aware that it is occurring
3) God doesnt intervene in the occurrence
A direct contradiction is implied in each of the three examples: The first is not compatible with Gods omnipotence. The second is not compatible with Gods supposed omnipresence and omniscience (although, omnipresence and omniscience are generally considered a part of omnipotence). And the third is not compatible with the concept of a loving God.
The contradiction doesnt depend upon morals, what we think is wrong, human emotions, or what God ordains.
P1. If God were all merciful there would be no suffering.
P2. There is suffering
Conclusion: Therefore there is no all merciful God.
P1 is a necessary truth; P2 is evidential. In order to disprove the conclusion it must be shown that P1 is false, i.e. that there can be suffering where there can be no suffering, which is absurd, or likewise to say suffering does not exist, which would be equally absurd since the objector acknowledges its existence in attempting to answer the problem of evil.
The contradictions that arise in God's stated attributes use the same logical format that gives us the concept of God, ie that (if he exists) he exists necessarily etc. So it is nonsensical to accept the defining essence of God and then deny it when it comes with a different logical expression but with the same structure and formality. An omnipotent creator, God causes and conserves the existence of everything. And a benevolent, loving God cannot send evil into the world. Those two sentences are analytic, that is to say each expresses the truth as subject and predicate, without having to go outside the proposition. And they are true because they cannot logically be false.
And the free will defence again (the main point Ive been arguing)
But if God is the omnipotent creator, the cause of all existent things, and evil exists, then it does so only because God causes and sustains its existence, since nothing can exist independent of Gods will. And this brings us back to the inconsistent triad and the classic argument for the incompatibility between Gods omnipotence, benevolence and the problem of evil. The notion of an omnipotent, infinite, perfect and all-loving being that punishes his finite, imperfect creation for their created faults is an absurdity that stands on its own. But when the Free Will Defence is introduced, the apologetic compounds what is already illogical, since it wants to say that it is better for an omni-benevolent God not to be omni-benevolent than for humans not be able to choose evil. It also informs us that an ability to inflict suffering is of a greater moral worth than having that ability withdrawn or made impossible. Aside from the obvious contradiction, that argument is misleading since it assumes that free will must necessarily imply the existence of evil. It does not! Once again we need a timely reminder that if God exists then nothing exists but what God brings into being.
Of course it cannot be said that free will necessarily implies evil, because that presumes to dictate what an omnipotent being must create, which is contradictory. And yet, if free will does include evil then it can only be because the omnipotent Creator makes it so. Now if we hypothesise that there is a creator God then of course it/he must have the power to bring worlds into being, and it follows that as we continue to exist it can also be said that such a Being conserves and sustains the world. Given the hypothesis, neither of those premises is self-contradictory. We can even say the Being is omnipotent; and while this assertion cannot be inferred from the fact of our existence, as the Being need only be sufficiently powerful to create our existence, there is no contradiction in our supposing it. But what happens when we say God is love, or God is perfectly good and moral? Here we have contradicted ourselves; for we know that evil is factually evident? For if everything that God created was good, then nothing created by God was evil. So if every existent thing is good, then no existent thing is evil. Yet there is evil! Therefore, as some existent things are evil then not every existent thing created by God was good. And thus it is demonstrated that God the Creator is not a wholly good and beneficent being.
The above only apllies to classical theism, but there is no reason why a Supreme Being should be omnibenevolent or merciful. And in fact doesn't an indifferent God fit more acurately with reality?