Why did God allow the Holocaust, Pearl Harbor, the Hiroshima and Nagasaki bombings?

Because He created humans with free will. We can decide whether to live according to God's will, or reject His will and choose evil, both in our personal lives, and on a much larger scale. Would you want God reaching down and smacking you every time you decide to do something that is not in accord with His will?

The same reason he allows any human travesties. Perfect wasnt good enough for Adam.

Read the first three chapters of the Bible. 

See also....

James 4:1-4 — What is causing the quarrels and fights among you? Don’t they come from the evil desires at war within you? You want what you don’t have, so you scheme and kill to get it. You are jealous of what others have, but you can’t get it, so you fight and wage war to take it away from them. Yet you don’t have what you want because you don’t ask God for it. And even when you ask, you don’t get it because your motives are all wrong—you want only what will give you pleasure. Don’t you realize that friendship with the world makes you an enemy of God? I say it again: If you want to be a friend of the world, you make yourself an enemy of God.

Did any of them truly ask Jehovah for help? What about the nations who did these things: Did they ask Jehovah for a better option? Don't blame Jehovah. Blame those "children" who claim they can do better then Jehovah.

There are many other man made disasters that could have happened but didn't -- like the Cuban missile crisis, WW3, etc. How would you know if God intervened or not? While God allows us to destroy each other, how about taking into account that God also allows us to continuously help each other? There is a reason why God commands us to love each other. Because we're being placed in charge of managing our natural world while we're here and able. The disgusting thing about some of us is that if our lives are nearly perfect, we would still look for imperfections and use them as excuses to excessively hate God. 

Accordingly, God's assurance is not the perfection of this life but the prospect of the afterlife. What we get depends on our deeds.

Free agency. 

God has to let us do good so he can bless and reward us.  He can't be arbitrary about these things; he is as bound by eternal laws as we are by natural laws.  He has to let us do good.

The problem is that the ability to do good is also the ability to do evil.  God can't stop evil without also stopping good, and that would destroy his plan for our happiness and salvation.  He has to let us do evil if that is what we insist on doing.  We would all be very sorry indeed if punishment were immediate or proactive.  God can normally step in only when entire societies become irredeemably corrupt.

Mankind's ills are man caused, and can be solved/resolved by mankind.

As Our Lady of Fatima has told us, war is a punishment sent by God for people's sins.  She predicted the end of WWI and the beginning of WWII.

You do know that the Lord God will make people who will want to dismantle all of the weapons we have in an era of 1000 years that Jesus will reign when He comes back. And Just because He is one person the number you cannot count will rise up against Him in the end of the 1000 years and they will be consumed with fire from...

Why does God let you perform injustice on some people . When you know you must obey Mat. 5:48 greek text

Because the creator is not a micro-manager.