The question of theodicy, for me (an atheist), is not so much “why does god allow so much suffering?” as it is “what is the nature of this god you believe in?”
The real contradictions I see are between the realities of the world, supposedly created and overseen by god, and the descriptions of their god by the faithful. They don’t mesh. The ancient Greeks were much more honest, I think, in their depictions of their gods. Greek gods were petty, arbitrary, powerful and mean-spirited. As such, they fit the world we live in.
Christians, Muslims and Jews all describe a god that is benevolent, just, omnipotent, and omniscient—which doesn’t fit our world one bit. If you’re determined to believe in a god, Zeus makes a lot more sense than the supposed Christian “heavenly father.”