As Epicurus is said to have said, what suffering shows is that EITHER that God is not benevolent OR that God is not omnipotent ─ or, of course, both.
Arguably, the Gnostics came up with an innovative - if rather "*out-there*" and weird - solution to this problem of suffering that @adrian009 poses.
I actually think it was reflection on this issue that was one of the main reasons for the emergence of Gnosticism and its controversial theology, in the first place
They circumvented your binary division here (bad God vs not all powerful God) by suggesting that the "first principle", the transcendent ground and cause of being Itself (the Forefather, or "Bythus" (Depth)) was not the creator-god of our universe.
For them, the god of this world was only a lesser, emanated and intermediary being: either evil in nature or simply ignorant of the Supreme Reality, who crafted an imperfect world that only dimly reflected the "pleroma" (the divine fullness which is true reality).
In the Valentinian Christian version of this Gnosis myth, they even adopted a monistic / idealist approach, contending that the material world with its deficiencies and suffering was an illusion dissolved by knowledge (gnosis) of God. They compared it to waking up out of a dream or seeing clearly once a fog cleared.
Suffering was tied to ignorance of the true nature of reality, which is that we are all in the "Totality", the fullness of the Father and not distinct from Him.
When a gnostic attained this liberating knowledge, the world of multiplicity and dualisms - good and evil, pain and pleasure - under its ignorant ruling Deity, would be understood as an illusion hiding the fundamental 'complementarity' of opposites in a fundamental wholeness: "Light and darkness, life and death, right and left are mutually dependent; it is impossible for them to separate. Accordingly the 'good' are not good, the 'bad' are not bad, 'life' is not life, 'death' is not death." (Gospel of Philip 53:14-23).
As St. Irenaeus stated in relation to the "heresy" of the Valentinian Christians:
"Since deficiency and suffering had their origin in ignorance, the entire system originating in ignorance is dissolved by knowledge (gnosis)" (St. Irenaeus [180 CE] Against Heresies 1:21:4 cf. also Irenaeus Against Heresies 2:4:3).
Thus, they were able to explain the existence of suffering - which they termed "deficiency" or "lack of knowledge" - without attributing it to the supreme "God" and making him evil, but rather viewing it as stemming from ignorance of the really Real on the part of humans and lesser divine beings like the Demiurge who rules the illusive world of matter. This also takes away the argument that God is not "all-powerful" (He is in this theology, the ignorance arises in us and we need to overcome it through knowledge of God).
So in this creation myth, the god worshipped as world creator is an ignorant being - a blind guide of the blind under him - who is either unaware of, or lying about, the true God who is Being Itself.
Human beings in this theology were encouraged to liberate themselves from both him and his creation/illusion, by realizing the divine spark within themselves and thus overcoming the deficiency/suffering caused by ignorance of Truth.
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