Not only is it not persuasive, it is not even particularly instructive. Why arbitrarily choose eugenics as the point at which we mounted the slippery slope?
In most discussions like this, the first one to mention the Nazis loses. This is an exception to that rule.
I would suggest that when considering controversial or even questionable programs of this sort, it is generally instructive to consider and reflect on how similar programs originated and have been used before. Are all uses and programs going to end up as their predecessors? No. But do the underlying philosophies and former applications provide warning (or hope) when considering whether to engage in new manifestations of older practices? Yes. History is full of reincarnations, and when a former manifestation results in something as horrific as the medical execution of the handicapped, infirm, retarded, and "impure," Id say a good look at the rationalizations for how we got there is in order. When the same underlying justifications are again trotted out to rationalize certain kinds of abortions for certain kinds of people, Id say those justifications demand another hard look. Simply because there are other factors and other philosophies that pushed Germany down the slope doesnt discount it as a reminder of the dangers of a social-reform eugenics program and the kinds of tragedy that can result.