Problem of Suffering: Doug's Rebuttal

A reader who I will call 'Doug' had a rebuttal to my Problem of Suffering critique:

Your argument seems to be that gratuitous suffering cannot exist because a God who is omnipotent, omniscient, and omnibenevolent would not allow it. The problem is that the presence of gratuitous suffering is the test; we must establish that it does or doesn't exist without deferring to the conclusion we're trying to establish. We can't just hand-wave away suffering as 'not gratuitous' by simply assuming it must have some purpose if we are right that there is a God. It's an empty argument, and one instantly seen-through by anyone with a passing knowledge of the logical fallacies.

You seem to have misunderstood what my argument is. It is not simply that God "would not allow it." Rather, it is that gratuitous suffering stands in contradiction to a God whose attributes are omnipotence, omniscience, and omnibenevolence—in the same way that an 'immovable object' stands in contradiction to an 'irresistible force'. Either gratuitous suffering exists or God exists; it is logically impossible (by the very definition of the terms involved) for them to both exist. That's the sticking point. It's more than theologically untenable; it is logically impossible. This is why presupposing the existence gratuitous suffering commits the question-begging fallacy.