He had no choice. You know in the US America put Japanese and some Germans in camps? Conditions were worse too. In Auschwitz, they had a soccer team, hospital, kitchen, brothel, swimming pool etc. the reason why deaths happened in Auschwitz was because the alias bombed raid roads, and other areas so food and medicine was impossible to get there. They starved and died of typhus. the true number was more like 200k-300k. If you look up world jewry population within 10 years the population actually increased, There was no official document that Hitler wanted to kill Jews, Hitlers Doctor was Jewish, again Hitler wanted them shipped to Palestine (Haavara agreement) some went, most stayed.