The fact that merely questioning the accuracy of this historical claim will land you in prison in numerous countries is enough to invalidate its veracity and tell you everything you need to know about it. No other historical event gets a similar treatment by nations anywhere else in the world. The holocaust is treated as gospel and questioning it is tantamount to heresy punishable by imprisonment, social castigation, and being made a societal invalid. Good luck finding a job or starting a business anywhere and building a life with the reputation of "anti-Semitic holocaust denier" hanging around your neck. People will treat you like a pariah and leper.
The logistics, resources, and mathematics simply don't add up. The energy and time investment to construct incinerators and systematically execute millions of people, while a war is raging on multiple fronts with its own resource requirements, is strategically stupid, not to mention impossible. The best we can determine is that there were concentration camps and most likely around 100k-250k Jews died, but not by systematic execution. Most starved or were worked to death.
The reason for the holocaust lie was simply to garner global sympathy in support of creating the state of Israel. And it worked.