First, a correction: If God exists, then why does He allow evil to exist? This is the real question that we want to ask, not "why does evil exist?" Implicitly, we are accusing God of allowing unjust suffering and victimization. We question His motives for such allowance. We question his benevolence. We question whether he has the ability to intervene. Some of us even surmise that evil exists because God is evil Himself. For those of you who have gone beyond implicit to explict accusations, congrats for moving onto what I call ignorant pontificating.
Why didn't God stop the Holocaust? Why doesn't he stop rape? Why doesn't he stop murder? We also might as well ask why God doesn't stop gangsta rap, corporate theft, cheating on tests.
While we're asking, why doesn't God stop abortion and human cloning? (If you think that's different, I want to know why. Will you defend those things, pulling out pragmatic rationalizations and preach about rights and Moreauean cures?)
What about the husband who just needs a little action on the side? Why didn't God turn him off? In the end, some if not all of us will at some point identify and sympathize with a perpetrator and even defend his/her act of evil. There goes our credibility.
Bottom line, arbitrary human indignation cannot demand that God do something to right what we particularly think is a wrong, precisely because we are endemically fickle. Humans are walking contradictions, spreading our ignorant pontificating about ultimate justice but wanting to exempt ourselves from it. We have lost all credibility to rage against evil or to accuse God of anything. Remember, in this world, one man's racism is another man's right to free speech.
In the Christian perspective, we will see God's intervention but at His appointed time and on His terms, not ours. I could say that it all began with Jesus on a cross, but then you might not tolerate an "unjust" raking of your conscience over the coals to think about the evil in your own life, and wonder why God doesn't stop me.
I have one: Why doesn't God strike all atheists dead? That would certainly remove all doubt and doubters concerning His existence.