Amateurs who play chess think one move ahead. Good amateurs think two moves ahead. Chess Masters think 10 or 20 moves ahead.

Holocaust Denialists are amateurs who think one move ahead. The Germans were professionals who were thinking a dozen moves ahead.

Why would they waste fuel? Ridiculous!

Amateurs think that it was wasting fuel. Professionals know that hiding the evidence of the crimes was far more important to the Nazi leadership, especially when they realised that they might lose the war. PR and covering your ass was as important then as it is now.

Amateurs think that you need a huge amount of fuel to burn bodies. Sure, if you do it wrong.

Professionals know that if you design the fire properly, allow plenty of air, and keep it running 24 hours a day, it doesn't need much fuel.

Domestic crematoria burn one corpse at a time. Efficiency is not needed. A lot of fuel is wasted heating up the crematorium from room temperature, the body is cremated, then it is left to cool again. Very inefficient, but people do insist on not mixing up their loved-ones' ashes with those of other people.

The Nazis didn't care about that. They built crematoria designed to run continuously, able to take dozens of corpses at a time. Much, much more efficient. But not efficient enough: they had too many corpses even for those. So they designed open-air burning pits that could take hundreds of corpses at a time, and run 24 hours a day for weeks at a time, operating on mostly human fat with a little bit of oil and alcohol to get the fires started.

German ingenuity and engineering excellence applied to the problem of burning thousands of corpses a day. They were professionals, not amateurs. They knew how to build a self-sustaining fire using the proteins, fats and oils in the corpses as fuel. The problem isn't that much different from burning green wood: get the wood hot enough to evaporate the water, and it will catch fire and provide enough heat to evaporate the water from the next piece of green wood.

They didn't need a lot of fuel, just enough to get the fire started and ignite the first few corpses. Even emaciated bodies contain enough protein, oils and fats to burn itself to ash, provided you can get the fire hot enough to start. By interleaving the bodies of healthy victims and starved victims, and collecting the molten fat that ran off and pouring it back over the bodies, the fires were self-sustaining with only a modest amount of fuel needed to start the process.

they had stockpiles of nerve gas yet they supposedly used insecticide that can't kill humans

Amateurs think that "nerve gas" is better just because it sounds scarier. Professionals know that using commercially available insecticides available off the shelf in 1940 was better.

The Tabun nerve gas had many problems:

• It was expensive and difficult to make which is why Germany only managed to make 12,500 tons.
• They had severe problems with it degrading during storage.
• The army wanted to keep it as a deterrent in case the Allies attacked with poison gas.
• It can be slow acting: even a fatal dose can take 1-2 hours to kill a person.
• It required special training and equipment to use, and was very hard to adapt to mass murder.

Cyanide-based Zyklon-B was much cheaper, could be purchased from civilian manufacturers as a ready-to-use product, was much easier to handle, and more certain in its effects: it killed in under 20 minutes. It was anything but inefficient. It was easy to handle, could be used with a minimum of training, it was much safer to dispose of the corpses (the Sonderkommandos typically only needed to wear gas masks to handle the dead).

Despite what you say, it was absolutely deadly to humans. It produced cyanide, a deadly poison. It was not one of our modern, 21st century insecticides that are relatively safe to humans. It was old-school.

Also, I daresay that Hitler got a kick out of using insecticide to murder people that he thoughts of as parasites like lice and ticks.