not discouraging further discussion here, but fyi, there's a FAQ section on the topic you should check out

• Holocaust Denial

They "who" and "why" mostly comes down to various right wing extremism.* If its Nazism, Islamism or another political ideology. Most of them have antisemitism in common. The motive might differ, for example modern Neonazis who deny the Holocaust want to take blame away from the original Nazis, they want to make Nazi-Germany seem like they weren't that murderous.

For Islamists the motive might be the "Victim debate". For a lot of Arabs it seems as if Israel can do what they want because the West still has sympathy for them due to the Holocaust. This then gets interwoven with classical antisemitic conspiracies and gets denied, so Israel is just many states among others. Also the tought that they (Arabs) are the real victims, by Imperialism or Israeli expansion.

The Israeli state takes a lot of moral legitimization from the Holocaust, and its creation is closely tied to it. So undermining the legitimacy of the Holocaust, is undermining the moral legitimation of the Israeli state. E.g. Iran is a perpetrator of this.

So in my opinion, Holocaust denial today has two main flows, 1) the glorification of the past/ Nazi Germany and b) an indirect attack on Israel.

*Since the 60ies there is also a lot of leftist antisemitism, but I don't know about any self-proclaimed leftist who'd deny the holocaust, no matter their stance on Israel.

One reason is that Nazi Germany referred to the Holocaust euphemistically in official correspondence and made a sincere (albeit impossible) effort to cover it up towards the war's end, which created enough "discrepancies" for neo-nazis to exploit and fool a disturbingly high number of non-nazis.

As for the rest... if Hitler was a genocidal monster, then nazism, and by extension racism, are bad. And these ideologies were once widely-held, and there's more than a little cognitive dissonance that keeps some people from letting go of even the most discredited or awful ideas, and a lot of stuff still floating around in western culture about how certain groups of people are bad that some people latch onto. There's also a lot of social change that happened post-WWII - decolonization, civil rights - that some people strongly opposed. Which shouldn't be surprising - if the old order didn't have supporters, it wouldn't have had power in the first place.

According to the National Socialist White Peoples Party, as quoted on the Nizkor Project (a wonderful resource on debunking this nonsense) "The real purpose of holocaust revisionism is to make National Socialism an acceptable political alternative again." Seriously, go to nizkor.org - it doesn't mince words but it does a great job of exposing holocaust denial for what it is.

It also doesn't help matters that neo-nazis have always had a strong web presence - anonymous and psuedonymous communication has allowed people with socially unacceptable views or interests to find each other, sometimes it can be liberating, other times, like in the case of stormfront, it can be awful. The KKK in particular jumped onto the internet very early and white supremacists spammed with a ton of determination even in the usenet days. And in doing so, they spread this conspiracy theory far and wide.