This question has been previously answered on Quora,
In an interview I did with Yehuda Bauer in Israel, he stated it succinctly:
“The denial of the Holocaust is due to the inability of a society to accept what it did.”
Certainly denial, prejudice, and many other factors contribute to the series of groups and people who deny the Holocaust.
One of the factors used by “researchers” online is the actual number; the original 6 million figure was an early estimate based on general population numbers, and is not one that even Holocaust historians quote.
It is an estimate.
And in estimates, and the chaotic end of WWII, with the Nazis blowing up evidence to cover it up, makes it hard to get a specific number.
This brings the “scientific” claims that the numbers are bunk, and with the Polish count at Auschwitz reduced significantly ( see Plaques Changed at Auschwitz-Birkenau), many try to use this to justify the denial claims that the numbers are too high, and exaggerated in their opinions.
By reducing the Holocaust to a supposed count based on accuracy and numbers, the deniers find solace in the lack of exactness and then take a leap to say this proves that the Holocaust never happened.
If you can’t deal with what happened, or live with hatred in your heart, it’s easy to label things as you want, which is the source of most denial, veiled as scientific research but really built on any doubt or supposed inaccuracy in numbers.
The Holocaust is not a game of numbers, it is a historical event that to this day affects us all, in a society where more and more of the underlying hatreds come to light.
I agree with Dr. Bauer, that denial of the Holocaust is in essence, a denial of what happened…the real denial is the inability to accept AND change what it did, which frustrates many scholars even to this day.
Sorry that no one can give you an exact answer to their motivations, they vary greatly between groups.
One of the primary motivations is to avoid responsibility as a society, and to explain why so many years later, we as a civilization haven’t really progressed to the point where we deal with the core truths the Holocaust has to teach us.
Denial veiled as “prove this” is an easy way out, and many choose the easy way out rather than dealing with the causes, and effects, the Holocaust has on us all to this day.