Holocaust denial started in Nazi Germany itself.
The Holocaust was a closely guarded state secret that was rarely committed to paper and when it was it was always marked “Geheime Reichssache” (Top Secret), requiring special handling and destruction to prevent capture by the enemy.
Hitler was afraid that even within Nazi Germany, while many supported the persecution of the Jewish peoples he worried that most would balk at the thought of wholesale murder. He also considered the populace of the remaining Jewish peoples under his command, Jewish resistance wouldn't form and be a thorn in his side until they were aware of what was being done to their fellows and even in the camps themselves, soldiers were deemed more necessary to be at the easter or western fronts than on guard duty so the guards and leaders of the "final solution" used codes and euphemisms to cover what they were doing.
For example, “action” (Aktion) referred to a violent operation against Jewish (or other) civilians by German security forces; “resettlement to the East” (Umsiedlung nach dem Osten) referred to the forced deportation of Jewish civilians to killing centers in German-occupied Poland; and “special treatment” (Sonderbehandlung) meant killing. In short Hitler did his damned best to keep it under wraps.
At the same time the Allies had started a propaganda campaign against the Nazis to drun up support and galvanise resistance to them and bolster the war efforts at home, these included the claims of German soldiers bayonetting babies to disfiguring woman and so on. After the war though, many of these claims were discovered to be false and in a world without mass media this would create doubt in some peoples minds on all the other thinhs the Allies discovered while liberating the camps. To Johnny "Stayathome" back in America the claims that millions of corpses were found sounded like more false justification. On top of that, many people thought that the numbers were being exaggerated to build goodwill towards the Jewish people (in lead up to the creation of Israel) and so many people who deny the Holocaust argue that the supposed “hoax” served above all the interests of the State of Israel.
Holocaust denial is, for these people, also an attack on the legitimacy of the State of Israel. Holocaust deniers want to debate the very existence of the Holocaust as a historical event. They want above all to be seen as legitimate scholars arguing a historical point. They crave attention, a public platform to air what they refer to as “the other side of the issue.” Because legitimate scholars do not doubt that the Holocaust happened, such assertions play no role in historical debates. Although deniers insist that the idea of the Holocaust as myth is a reasonable topic of debate, it is clear, in light of the overwhelming weight of evidence that the Holocaust happened, that the debate the deniers proffer is more about antisemitism and hate politics than it is about history.
For an insight into propaganda tactics and just a fantastic historical book on Nazi Germany I'd suggest reading "The rise and fall of the third Reich" by Wiliam L Shirer (one of my favourites) or for direct material on holocaust denial I'd suggest "Deniers of the holocaust: who they are, what they do, why they do it" by Ted Gottfried
Hi, there is a collection of threads on denialism in the FAQ here - https://www.reddit.com/r/AskHistorians/wiki/faq/militaryhistory/wwii/nazigermany#wiki_holocaust_denial