Villawagen, the reason is that until 1960 Cyprus had been a British colony. The 82% of Cypriots, who are Greeks like the Greeks of Crete, Rhodes and every other island, wanted to be decolonized and join the newly founded Greek state, like the other Greek islands did. For example Crete joined the Greek state in 1913, not much earlier. Until then liberation meant that, since no island in Med sea was independent. (Cyprus was the first in 1960, and the only other is Malta)
However the British didn't like the idea of Cyprus going to Greece as this wouldn't serve their strategic interests (wouldn't be able to keep 2 so huge bases that way) so they got the Turks into the game and forced GCs to accept some semi-independence with things that exist in no other truly independent country, such as armies from foreign countries being stationed here (either we liked it or not), the "Guarantor" rights, and a several other crap that couldn't possibly work out.
So Greek Cypriots were screwed, and what they got to keep was the anthem.
Of course today personally I would support for Cyprus to have its own separate anthem as things have changed since the 60s, but I told you all this so the next time you will hear Cyprus play the Greek national anthem it will not sound that strange to you.