Why Was There a Holocaust and What Is Judaism's Attitude Toward the Nazis?

In this article, we will discuss three issues:
1) Judaism’s attitude towards the Nazis.
2) Why the Holocaust occurred according to the Torah.
3) Which moral view of the Holocaust is more appropriate, the atheist [as distinct] or the Jewish perspective.
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Let's start with the first issue, which also answers the second.
We were taught by the Sages
This sentence holds deep philosophy. People who sin are punished by those who chose to sin. The German nation always hated us and wanted to harm us, but if we had adhered to our G-d, they could never have harmed us. The proof: the Jewish people have survived beyond the natural laws of history for over two thousand years. While giant cultures like those of Greece, Rome, Babylon, and Persia have disappeared entirely, the Jewish people have survived even under persecution and exile. Naturally, the Jewish people should have been wiped out long ago, especially when being chased around the world.
Mark Twain, who visited Israel in 1867, wrote among other things:
"If statistics are correct, the Jews constitute but one percent of the human race. It suggests a nebulous dim puff of stardust lost in the blaze of the Milky Way. Properly, the Jew ought hardly to be heard of; but he is heard of and has always been heard of. The Jew stands out as an amazing example among the nations. The Jewish commercial importance is perhaps larger than the rest of the world’s proportionately to their population. Its contributions to the world's great individuals in literature, science, art, music, finance, and medicine, even also the profound learning, outweigh by far any other population. He has made a marvellous fight in this world, and has done it with his hands tied behind him. He could be empty and hollow within, and we would excuse it. The Egyptians, the Babylonians and the Persians rose, filled the world with sound and splendor, then faded to dream-stuff and passed away. The Greeks and Romans followed, and made a vast noise, and they are gone. Other peoples have sprung up and held their torch high for a time, but it burned out, and they sit in twilight, now, or have vanished. The Jew saw them all, beat them all, and is now what he always was, exhibiting no decadence, no infirmities of age, no weakening of his parts, no slowing of his energies, no dulling of his alert and aggressive mind. All things are mortal but the Jew; all other forces pass, but he remains. What is the secret of his immortality?" (Mark Twain, Harpers Magazine, Sept 1899)
"...Indeed, by the materialist and positivist criteria, this nation should long ago have passed away from existence. Its existence is a mysterious and miraculous testament that this nation's life operates through ancient decrees...".

(Russian philosopher Nikolai Berdyaev 1936, The Meaning of History pages 86-87).
"What is a Jew? This question is not as strange as it might initially appear. Let's see what kind of special creature it is, that all the rulers of the world and all the nations have insulted, oppressed, exiled, trampled on, persecuted, burned, and drowned, and he, despite their efforts, continues to live and exist. What is a Jew - who was never successfully tempted by all the allurements that his oppressors offered, just to abandon his faith and forsake the beliefs of his ancestors? A Jew is a symbol of eternity. One who could not be destroyed by slaughter or torture; neither fire nor the sword of the Inquisition was able to destroy him. He who first proclaimed the word of G-d to the world; he who preserved prophecy for so long, and handed it on to humanity; such a nation cannot disappear. The Jew is eternal - he is the embodiment of eternity.". 
(Leo Tolstoy, from an article published in Jewish World - London 1908).
We do not adhere to the views of these philosophers and thinkers, and yet these famous Gentiles understood it. Hashem guards us, and this is the secret of the eternal existence of the Jewish people throughout history. 
This secret cannot be explained naturally at all because even mighty empires have disappeared, much less small people who were persecuted (and considering assimilation, coupled with the difficulty of conversion to Judaism - compared to the Crusaders and missionaries in Christianity) shows that from any natural perspective, the Jewish people should have disappeared. Who would have believed that Gentiles would go to the ends of the world to kill Jews? Did you know that Hitler was on his way to kill all the Jews in Israel, had he not failed in Russia? 
And behold, in the Psalms (83), it is written what the Gentiles say every generation: "Come, let us wipe them out as a nation, so the name of Israel may be remembered no more." On the other hand, it is promised to us in the Torah (Leviticus 26:44): "Even when they are in the land of their enemies, I will not cast them away, nor will I abhor them to destroy them utterly and to break My covenant with them, for I am Hashem their G-d." And indeed, that is how it is: Haman the wicked tried to destroy the entire Jewish nation and failed. The Greeks and Romans tried to erase the Jewish identity and failed. Christians tried to convert all Jews by force and failed. Hitler wanted to eliminate the Jewish nation and failed too. Can anyone see this as mere coincidence?!
The Creator always guarded the Jewish people, as long as the Jewish people walked in His ways. But when the Jewish people abandon their G-d and rebel against Him, the providence is removed from them, and their enemies can harm them. The Nazis were sent because of the sins of Israel, not because G-d wants to punish or harm His children. There is a system of justice in the world, of which we only see a part, and everything works according to that divine plan. So actually, our wrong actions brought the Nazis to hurt us, just as human wrongdoing brought the flood to the world, just as Israel's sins brought the destruction of the first and second temples. Every act has consequences and results. 
Such are the laws of nature, so are the laws of creation: if a man jumps into fire or touches it – he will be burned and hurt, just as when Israel sins deliberately – its enemies hurt it.
Thousands of years ago, Hashem promised in the Torah (Leviticus 20:26): "And I have separated you from the nations to be Mine" – the Sages explained in the Talmud "If you are separated from them, then you are Mine, and if not – then you are with Nebuchadnezzar and his friends" (so explained Rashi on the verse). As long as the Jewish nation clings to its G-d, even great nations cannot harm it (and even a few Jews can defeat many and mighty Gentiles). But when the people of Israel rebel against the Creator, deny Him and try to imitate the Gentiles, they also become given into the hands of these Gentiles whom they admired. Jews wanted to emulate the Germans, to be like them, so they truly became theirs, and the Germans chose to kill them.

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