The part about the lesson from Holocaust being that this can and does happen elsewhere - that is my "favourite" part. To extrapolate on this a bit: The Nazis didn't invent the concentration camps - the Brits had used them in South Africa against the Boers, and the USSR had its gulags, the last of which apparently closed in the late 1980s. The genocide against the Jewish population in Europe was neither the first nor the last in history. And so on.
When you think of it that way, that the Holocaust is unfortunately not so unique even in exclusively human history, then it becomes a little bit easier to see that what humans are doing to animals is very similar.