1) Events have happened in the world that are such that any person able to prevent them would be morally obligated to do so.Chris has emphasized here the concept of moral duties or moral obligations; I think this approach to the PoE is very important, and highlights a basic starting presupposition that some Christians may subconsciously hold: that God has no obligations or duties towards its creation(s). Kant's formulation of the categorical imperative was focused here, on what we are obligated to bring about by the nature of moral normativity. He argued that we must always act in such a way that our behavior is compatible with a sort of absolutism; or, that we can only justify our moral behaviors if they are universally true and correct.
2) Premise (1) is logically incompatible with God defined as an all-powerful, morally perfect being.
3) Therefore, God does not exist.
Premise (2) I take it, is simply a fact of logic: to be all-powerful is to be able to prevent the sort of events described in (1), and to be morally perfect is to fulfill all of one's moral obligations, so if there were a God so defined, there would be no such events as described in (1).
As for (1), it appears to be almost universally agreed upon. A few decades ago it was reported that a woman named Kitty Genovese had been murdered and no one had done anything to stop it even though dozens of people had heard her screams. The story provoked some deep-soul searching and discussions about human psychology, all of which took for granted that the right thing to do had been to stop the murder. The international community has been harshly criticized for failing to do more to stop the Rwanda genocide. The current administration had been harshly criticized for failing to do more to rescue people from Hurricane Katrina.
This is where the disconnect occurs for believers in God.
While they will heartily agree that they are morally obligated to care for and protect their children from harm, they hold no such absolutism about this moral issue towards God. God can do whatever it feels like doing -- arbitrarily deciding to protect this or that prophet while at the same time neglecting a massive proportion of the earth's population. When they claim that God has to give us free will, they commit petitio principii: they are claiming that God's first obligation is to allow its creation to be free, rather than acting on behalf of the creation's best interests.
This logic certainly would not apply to the parent-child relationship, and most believers would agree to this. They would almost certainly agree that any parent who allowed his toddler to run through the house with scissors was not a moral, good parent, despite the justification offered by said parent that, "I just wanted to maximize little Johnny's freedom!"
We've trodden this ground before, of course. But it is helpful to frame the argument in terms of moral duties, because the immediate presupposition of God's lack of moral obligations, on the part of many theists, renders this God's "goodness" fatally flawed and illogical.