Student or Learner
The primary motivation for most deniers is anti-Semitism, and for them the Holocaust is an infuriatingly inconvenient fact of history. After all, the Holocaust has generally been recognized as one of the most terrible crimes that ever took place, and surely the very emblem of evil in the modern age. If that crime was a direct result of anti-Semitism taken to its logical end, then anti-Semitism itself, even when expressed in private conversation, is inevitably discredited among most people. What better way to rehabilitate anti-Semitism, make anti-Semitic arguments seem once again respectable in civilized discourse and even make it acceptable for governments to pursue anti-Semitic policies than by convincing the world that the great crime for which anti-Semitism was blamed simply never happened—indeed, that it was nothing more than a frame-up invented by the Jews, and propagated by them through their control of the media? What better way, in short, to make the world safe again for anti-Semitism than by denying the Holocaust?
They are "denying" that the Holocaust happened.
It is safe to assume that if a primary motivation for X is Y, then X is also for (in favor of) Y.