This is probably the biggest question, and the biggest obstacle to trusting God, in Christianity. It's a legitimate question, and it deserves a thoughtful answer that honors the amount of pain attached to it. Disclosure: I am writing this while beset by the most physical pain I've experienced since post-polio syndrome started attacking my body with the "unholy trinity" of pain, weakness and fatigue. It hurts to stand, it hurts to walk. Every single step.
Why does God allow it? And my pain is nothing compared to the horrific suffering of millions around the world. Doesn't He care? Why doesn't He stop it—surely He can. He could stop it all with a single word. So why does He let innocent people—especially children, for heaven's sake—suffer?