It's closely related to the internet principle asserted by Mike Godwin in 1990, known as Godwin's law: "As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches 1."
No group is more prone to playing the Hitler/Nazi card than us pro-lifers. We use the term holocaust to refer to the millions of unborn children aborted since Roe v Wade in 1973. We talked about death panels during the debates about Obamacare. We compare the use of terms like fetus and "choice" to the dehumanizing language used for Jews and other undesireables.
Our opponents, naturally, accuse us of being intellectually lazy and alarmist, irresponsibily exaggerating contemporary threats to human life and unfairly demonizing those who don't share our views. Some prominent Jews object to our use of the term holocaust, saying that it diminishes the atrocites perpetrated by the Nazis and insults the memory of those Jews who perished.
Sensitive to these concerns, some pro-life persons are careful not to rush to Hitler comparisons and Nazi analogies when discussing pro-life issues. In a recent radio interview, for example, I was talking with Dr. Peter Wick from Villanova about Dr. Peter Singer, the prominent moral philosopher from Princeton whose utilitarian ideas include a tacit endorsement of infancticide and euthanasia as morally justificable under certain conditions.
Toward the end of our conversation, I mentioned the irony of Singer's views when considering his own parents were Austrian Jews who escaped the holocaust, and several of his grandparents likely died at the hand of the Nazis. Dr. Wicks rightly steered me away from the topic, not wanting to be exploit Singer's personal history and arguing that it's not wholly fair to compare Singer's academic ideas to actual Nazi atrocities. In retrospect, Dr. Wicks was right; I crossed the line.
At the same time, though, I disagree with the contention of abortion advocates that there is no analagous connecction between those who justify legal abortion, assisted suicide, and euthanasia, and the Nazi death camps. I suspect that this contention is rooted in the idea that Hitler and his henchmen were a unique incarnation of murderous evil--unprecedented and unrepeatable in human history.
Rather, Shirer believed there was some something toxic within the German culture that produced the despotic regime. According to Wick, Shirer believed "the people were guilty. Their history brought them to Hitler. These are beliefs he would carry with him for the rest of his life."
I'm no historian, but I tend to have greater sympathy to Shirer's view, if nothing else because of the vast social and sytemic machinery needed to facilitate the extermination of multiple millions of human beings. This was not something a few madmen could perpetrate without tapping into a latent anti-semitism and hubris within the nation itself.
I am also mindful of the phrase "the banality of evil" coined by Hannah Arenddt, the German-American political theorist (and secular Jew). After observing the trial of the former Nazi fugitive Adolf Eichmann, captured in Argentina in 1960, she came to believe "that the great evils in history generally, and the Holocaust in particular, were not executed by fanatics or sociopaths, but by ordinary people who accepted the premises of their state and therefore participated with the view that their actions were normal."
Ideas have consequences, and Hitler, his associates, and their propaganda machine tapped effectively into both the anti-semitic attitudes of some Germans (and frankly, other complicit Europeans) and the fashionable eugenics of the day to pursue their lethal final solution.
To me, the Hitler card fails when played for some ridiculous reason, such as "You love dogs, and Hitler loved dogs; when do you plan to start gassing Jews?" But when alluding to fundamental ethical ideas about who can and cannot claim the right to life, then it's fair game to point out that the Nazi extermination of actual human beings began with some of those same ideas, beliefs that continue to be manifest--vis a vis abortion--in lethal actions against innocent human life.
mirrors almost exactly the plot of Ich klaga en (English: I Accuse), a 1941 German film commissioned by Nazi propagandist Joseph Goebbels to help persuade the public to be more open to the idea of killing the disabled.
So people who shrug their shoulders at a Peter Singer, or this lady, or this guy, or this lady, beg the question--just what does it take to get compared to Nazis?