You don't hear that comment very much these days, but it used to be cited as an example of people who were deliberately blind, who refused to look at, or accept, some evil which they must have known about, or even that those who were pronouncing their ignorance were telling lies. Well, I have news for them: during World War II the average German, particularly the average German civilian, really did know nothing about the gas chambers.
For a start, there were no gas chambers on German soil. No, there were not! There were concentration camps. They were horrible places, and their death rate was very high. But, apart from some minor gas chambers at Ravensbrück, the actual gas chambers were restricted to the huge extermination camps, such as Auschwitz, Majdanek, or Treblinka, among others. And these were all on Polish territory, for the obvious reason that this was where the Jews were. Poland was the pre-war centre of Jewry. Half of the Jewish victims of the Holocaust came from Poland. On the other hand, 85% of German Jews had fled Germany by the time the war started.
And yes, a lot of Germans knew that Jews were being rounded up - hence the underground railway of gentiles who hid fleeing Jews or passed them on to safe houses. What they didn't know - and neither did the victims - was their ultimate fate. Deportation or imprisonment would have been the logical assumptions. The Holocaust was performed under a cloak of silence and secrecy. Again, the reasons are not difficult to divine. The Nazis didn't want to provide propaganda material for their enemies. Also, if the truth must be told, they were probably rather ashamed of it. But the most important reason was to forestall any action on the part of the victims, either of escape or resistance. Starting from October 1940, 400,000 Jews were herded into the Warsaw Ghetto, ill-treated and starving, then subject to mass deportations. In January 1943 they rose in revolt. Do you think they would have waited so long if they had known they were going to be gassed? It doesn't do to offer human beings the choice of fighting and probably dying, or not fighting and certainly dying. Human beings are more dangerous than rats, and even rats are dangerous when cornered.
Under the code words of "Nacht und Nebel" (night and fog), troops would descend on the ghetto, or some similar Jewish settlement, and herd the inhabitants onto rail cattle trucks, telling them they were being deported to the east as agricultural colonists. On arrival at (say) Treblinka station, they would be unloaded at double time and told it was a way station. Those who had time to read would have seen bogus timetables on the station walls indicating bogus trains heading farther east. Next, they would be herded into buildings set up to look for all the world like ablution facilities. Here they would each be given a towel and a bar of soap, and told to strip off, hang their clothes on a hook, and enter the shower cubicles. Some younger, fitter victims would be separated out to serve as temporary workers, but for most of them, the first thing they knew about their intended fate was when the showerheads were turned on, to emit poison gas rather than water.
Now, ask yourself: how much do you know about what goes on inside our own prisons? Probably you don't spend much time thinking about it. But at least you live in a democratic society. You know that prison sentences do come to an end, that freed prisoners can talk, that they have relatives, friends, and prisoner aid societies who may well speak up on their behalf. The press is still free. Members of Parliament can still ask questions. You assume that, if something really bad were happening, you would hear about it. Now, imagine you lived in a police state, where even asking such questions would result in your receiving an answer by first hand experience. What if you had other things on your mind - like where your next meal was coming from, whether your son would survive on the eastern front, or whether you yourself would survive the Allied bombing? You suspected that terrible things were happening, but some questions were too dangerous to ask.
And remember: we are looking at it all from hindsight, but nothing like this had ever happened before - at least not on European soil. ("Who now remembers the Armenians?" Hitler once said.) Who would ever have thought of gas chambers, and the deliberate extermination of a race, before the event? Perhaps you should Walter Laqueur's 1980 tome, The Terrible Secret, which describes how, time and time again, when Jews in occupied Europe itself were given first hand information about the Holocaust by those with direct experience, they refused to believe it. It was, after all, too horrible to be true. Auschwitz was a labour camp as well as an extermination camp, and in 1944 two inmates, Rudolf Vrba and Alfred Wetzler not only escaped, but made their way to England, there to lay the evidence before the Allied authorities and ask them to bomb the gas chambers. What did they do? They refused to believe them! They had been embarrassed about the lies told about German atrocities in the First War, and didn't want to see it happen again. Besides, it was too horrible to be true. The Nazis might have been wicked people, but nobody could be that wicked, could they?
If the victims and the enemy refused to believe in the Holocaust, I think we might allow the average German civilian a bit of slack.
Addendum. There was one exception, and it is rather telling: the "euthanasia" policy. I shall quote from The War of the World Twentieth-Century Conflict and the Descent of the West
The process was accelerated under wartime conditions; significantly, Hitler’s personal order authorizing the ‘euthanasia’ policy was dated September 1, 1939. The case of the asylum in Hadamar, north-west of Frankfurt, makes it clear just how overtly the Nazi state was now capable of committing murder. Between January and August 1941 more than 10,000 people were put to death there in a specially constructed gas chamber in the cellar, most of them mental patients transported from other psychiatric hospitals. Although the policy was supposed to be secret, local people knew perfectly well what was being done. As the president of the higher state court in Frankfurt reported to the Reich Minister of Justice, ‘even children call out when such transport cars pass: “There are some more to be gassed.”’ The smoke from the crematorium chimney was clearly visible hanging over the town. The personnel from the asylum were shunned by the local populace when they came to drink in local pubs after work. The Bishop of Limburg, in whose diocese Hadamar lay, followed Bishop Galen’s lead in protesting at what was being done. He too noted the absence of secrecy. Local schoolchildren referred to the buses that brought patients to Hadamar as ‘murder-boxes’ and taunted one another by shouting: ‘You’re crazy; you’ll be sent to the baking oven in Hadamar.’ A particular source of local concern was that elderly people would be next: ‘After the feebleminded have been finished off,’ local people were heard to say, ‘the next useless eaters whose turn will come are the old people.’ These complaints led to a suspension of the killings and the decommissioning of the gas chambers.