Why wouldn't people believe the Holocaust happened?
Well, it wasn't too hard to believe that a large political group: the National Socialists of Germany (Nazi for short), got a lot of people to think in a certain manner. Not just in Germany, but also influenced the world (ex: Vichy France, etc. etc.). Such influence extended even into the USA, across the Atlantic.
When those who fell under Nazi influence were told about the horrors of the Holocaust, its not too surprising that they'd deny the claims, because they felt like the Nazis were a good philosophy.
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I dunno. Its not very hard for me to imagine why people fall for conspiracy theories. You feel that a group you're in is getting attacked by another group, and you instinctively defend the group you're a part of.
A Nazi sympathizer will see the Holocaust claims as disinformation, and instinctively defend the Nazi philosophy.
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What is new and interesting, to me, is the speed at which conspiracies seem to spread _today_. It seems faster and more virulent than before. Understanding the mechanisms of social media is probably key.
We've had TV, Newspapers, even "fake news" (called Yellow Journalism in the WW2 era), and propaganda (Dr. Seuss / Disney made lots of wartime propaganda). That's not new at all. People understand that the media manipulates their viewpoints.
I think people have less of an understanding of how social media is shaping our society. Sometimes for the better, but in this topic of conspiracies... for the worse.