They sort of do. The government that conducted the pogrom against the Armenians is no more. It was overthrown not so long after the event.
To blame today's Turks for it, is like blaming todays Germans for Hitler's genocide, except that at some signifigent fraction of Hitler era Germans are still alive, while few pre 1920 Turks are likely to be alive).
Besides, most of us are decended from both pre and post slavery immigrants. Few have ancestors who fall in only one or the other category.
Good point! I was descended from French-Canadians, and immigrated to the US as an infant. I plan to use that if they ever demand 'reparations' from us!
Still, I imagine the Turkish population is more homogenous than the US population has been since 1920. I'd be willing to bet that a much higher percentage of Turks' ancestors were living in Turkey then, than you would find of current US residents' ancestors living here in that year. Otherwise, why would they be so very offended?