"A state composed of Turks, for Turks. The Armenians are not Turks....."
You haven't spent any time there, have you?
What does a Turk look like? What are the defining "ethnic" features of "Turkishness," if you will? There is no such animal.
I have met Turks with blonde, brown, and black hair, white, yellow, brown, and black skin, blue, green, and brown eyes, asian, caucasian, and negro features, and everything else that reflects a language that spreads from Siberia to Greece, and a former empire, that... well, just look at some maps. Figure it out for yourself.
This Armenian Genocide stuff is a load of crap anyway. There's an Armenian cemetary in my old neighborhood in Istanbul, for instance. Had there been some sort of genocide, that, and all record of it, would have been erased years ago.
I don't know enough of the history of Turkish nationalism, ethnic perception, and all those wonderful things, to give you an adequate answer. However, you are right in asking "what is a Turk?" This was a problem in Turkish nationalism, and it is a curious question (the idea of ethnic identity has haunted many nationalist movements ever since the inception of modern nationalism). It does not prove anything, however, as the Young Turks held a perception of a Turkish identity. If you do not believe me, simply gather up some books on the subject and read them. There are books from both sides (there is no such thing really as an impartial historian), and plenty of material on the internet (a good bit is sheer propoganda of course- everything from "Turks are vicous baby-eating killers" to "Armenia is the great Christian terrorists state!!- says Baptist preacher").
And you are right, I've never gotten to go to Turkey, but would love to some day. If you're really interested in my enlightenment, I'll give you my address and you can send funds for travel fare: )