Why ask about the Holocaust, why it happened? What about Somalia, Rwanda or even the streets of Chicago? Do we so quickly forget the small evils and only cry out to God when we see "great evil?" Why would He allow such horror?
As C.S. Lewis noted, there may be evil and sin in the world, but there also lies in this world for us the ability to love and have mercy, show bravery and intervene where we see such evil take place. Some people think they can imagine a world without sin and evil, and still have the chance to love freely, do real good and have a purpose in life. I cannot. God, it seems, thinks it worth the risk in order that we be truly free.
Any theist believes that God gave us certain rules. Religions differ on some, but most differ merely by degree (Don't kill people, or don't kill anything: don't kill. One wife or three: you can't take any woman you want whimsically). Many of the rules are alike: it seems some "truths" reflect a real Truth, something outside our own existence. The real Truth, the real Right. The real God.
These rules, which seem like Laws of Religions, in particular, the Word of God, isn't something He made up to bind us to despair, but are really simply expressions of Who He Is, and how the world works. Don't kill because 1) that life isn't yours to take, 2) it's His world, His Creation, in His image and 3) it disrupts the surroundings (society, relations, etc).
Don't have sex outside of marriage 1) not because He doesn't want you to have fun - He invented "that fun" and wants you to enjoy it - but He wants you to enjoy it in the fullness of the context for which it was created: loving, sharing, becoming one with someone else, friendship, honor, trust and charity; not to be selfish or greedy and seeking only your own pleasure or the smallness of what our physical pleasures seem to be. 2) Your actions have meaning and consequence. Fun SHOULD be had, but not at the expense of another - even if that person feels the same as you - you both still miss out on the fantastic fullness intended.
Etc etc etc.
God says don't break these rules because He doesn't want Holocausts, Rowanda or hurting children. On the other hand, since we have sinned - and make no mistake, they are our sins - it seems He did in fact make a world where the worst evil can be the cause for the greatest good. He saved you for that purpose. To do good, to honor Him. So we can love and be joyful. So there will be no more Holocausts.
"I dare not ask God why He doesn't do something about all the evil in the world because I fear He will ask me the same thing."
Christians believe we are the hands and feet, the body of Christ. Christ is the Head of the Church and that we exist for God, and for Him alone. If we are His hands and feet, why aren't we doing something.