~A Prophecy Of The Great Armageddon That Is To Come ~, page 1

I understand what you mean DenyAllKnowledge. You are missing a vital piece of information though that only people acquainted to a very large extent with greek history are familiar with.
The current state of Greece, is not what you would call a state inhabitted by Greeks. As a nation, we are a lot closer to oyr Byzantine identity, than our ancient Greek one. I hope you can understand what I mean:

In the ancient times, there were many different greek and non-greek tribes inhabitting the region. The greek ones were prevalent in the region the current Greece holds, and in the Minor Asian lands close to the Aegean. The rest regions were inhabitted by non-greek tribes, which were rather "converted" to Hellenism later: the Thracians, the people of Pontus, the Cappadocians.

The nation as it is now is what you would call "the Orthodox nation" and not
"the greek nation". There are an awful lot of Greeks that left Pontus, Cappadocia and the Aegean part of Minor Asia during the destruction of Smyrna in 1922, who refer to themselves as "Byzantine Greeks".

The name Greece is rather referring to geography rather than national identity. Our national identity is Byzantine, we feel all those 1100 years that forged the Eastern Empire are our history, and would definitely love to see our mighty past empire being re-forged with it's center in Constantinople. You may want to search on the "Megali Idea" issues of modern Greece of 1900+ (which ended in 1922 dreadfully), as it clearly describes what the Greek nation of the new state is.

This does not mean we are not descendants of the ancient Greeks. It is just that 2000 years of Christianity took their toll on our Hellenity and we are now a mixture of the ancient Hellenism and Orthodox Christianity.

I'm pretty sure however, you can understand what I mean about the mixture by looking at the ancient Romans and the current State of Italy: It is a mixture of ancient Rome & Catholocism.

If the Greeks are entitled to that land, then wouldn't it make sense to say that so is everyone who came before, and after them?

Before the Greeks the land was uninhabitted, when the Spartans first came to Constantinople (I prefer Constantinople, rather than the turkish "In-stam-bul", which is also greek, bu heh...) they found a colony by the name Byzantium, then Byzantium became Constantinople, and became the capital of the soon-to-be Byzantium, after the fall of the Byzantine Empire (1453) it came to the Turks. The only two people who can claim Constantinople are the Greeks and the Turks (and perhaps you would like to add the Romans who are ethnically Italians now and don't really care about the City).