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It is not about whether or not there is a god; but the fact they claim there is, claim this god is responsible for all, claim to be represtenatives of this god
This would mean that these "they" are claiming responsibility for, as you say, "all".
You will likely fail, but your case does have formal merit.
Another problem is that it would also mean that they are claiming responsibility for other things than suffering, and they could use your, as they would likely phrase it, "debt" as leverage to their case.
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"Everyone loves the dolphin. A bitter shark - emerging from it's cold depths - doesn't stand a chance." This is hyperbol.
"Run, Jump, Fall, Limp off, Try Harder."