David Irving is mercantile scum who cares about making money and selling his books. He does not care about the proper historical method despite all of his pretenses.

In their book Denying History: Who Says the Holocaust Never Happened and Why Do They Say It?, Michael Shermer and Alex Grobman also postulate that Irving has more venal and personal reasons for his denialism than just being a Neonazi sympathizer. Although Irving was never part of the official historical profession, he does seem to take particular relish in using his books to thumb his nose at the "professionals" who have rightly rejected his work. In letters defending himself in the run-up and during the Lipstadt trial he took his identity as a non-professional historian as a badge of honor. Sherman and Grobman also note he has to an extent been trapped by his denialism, but this is a very lucrative cul-de-sac. Looking at Irving's current career, they observe:

Seemingly, the more he revises the Holocaust, the more books he sells and the more lecture invitations he receives from denier and right-wing groups. The irony is that he appears, in our opinion, to have little respect for the people who constitute his most receptive audience, an audience far outside the mainstream academy. He told the journalist Ron Rosenbaum [in the book Explaining Hitler]: "I find it odious to be in the same company as these people. There is no question that there are certain organizations that propagate these theories which are cracked antisemites." But, he adds, "what else can I do? If I've been denied a platform worldwide, where else can I make my voice heard? As soon as I get onto regular debating platforms I shall shake off this ill-fitting shoe which I'm standing on at present. I'm not blind. I know these people have done me a lot of damage, a lot of harm, because I get associated with those stupid actions."

What is apparent in the Rosenbaum quote is that there is a strong undercurrent of self-pity in Irving's defense of the path he has taken.

Whether he likes it or not, he has thrown his lot in with various far-right wing groups. And for all his pathos about an ill-fitting shoe, this has been a very lucrative deal for Irving. At one point in the aughts, he managed to rent out an apartment in Queen Anne's Gate that cost £6,000-a-month. His denialism has a built-in audience to buy his books regardless of their quality or pay for him to speak at various lectures. Established authors working in the publishing industry like /u/mikedash can tell you more about the often cutthroat world of publishing and Irving is really following the path of least resistance for an author. His books all have roughly the same content (Hitler maligned, Churchill bad, Communism worse, Allies pursued Carthaginian peace, etc.) and part of how he makes a living is to sell yet more reprints of his earlier works like Hitler's War. Selling the same material to the same audience is tricky, but denialism is one way to accomplish this.

Irving was also a pioneer in online hate and the Institute for Historical Review transitioned very quickly from a costly print journal to a cheap webpage (and don't give them hits, but take it on me, their webpage design is very dated). Like its descendants such as Stormfront or 8chan, the IHR is as much about hawking the domain owners' merchandise as it is about carping on Zionist control of the media.

So why does David Irving deny the Holocaust?

The evidence suggests denialism makes him a lot of money and gives him fame his work would otherwise not find.

While it addresses Holocaust denial in general and not Irving's specific claims, you may find /u/CrossyNZ's answer here helpful to you, though the whole thread is really good. /u/kieslowskifan has also answered a variation on your question in the past. /u/commiespaceinvader led a really good "Monday Methods" post accompanied by well-written comments.

More FAQ entries about Holocaust Denial can be found here.