During the 2004 referendum a psychologist commented that Cyprus was like a community with schizophrenia and split personality.
Probably thats because he was crazy.
Most Cypriots on both sides voted in the referendum in a perfectly logical way. The Annan plan was a a pro-Turkish plan made by the Anglo Americans (Turkey's allies) and it satisfied the 99% of the Turkish demands while not only it didn't solve the problems of Greek Cypriots, on the contrary it legalized the crimes against us.
Therefore most TCs voted in favor of that plan since it suited them and most GCs voted against that plan since it didn't solve their problem.
The result of that referendum was perfectly logical and it could be very very easily predicted by anybody with more than a gram of brain. (in fact we all knew what the result would be months before). The schizophrenics are those that expected a different result.
As far as the "identity crisis" goes, there isn't any. In Cyprus we have Cypriots with Greek, Turkish or other ethnic background, and the great majority (of GCs at least) feel as Europeans as any other European.
The way you put the question is as if we have to choose between being European, or being Greek(or Turkish etc) or Cypriot. This is not the case. We are a European country with people from different ethnic backgrounds. As simple as that, and it is nothing strange or unique either.
The only thing that could be misunderstood as "identity crisis" is the claims of the pseudo state, that on one hand they already have a separate country which they fully support, and on the other hand what they support is unification. Obviously this 2 claims are contradictory, but the reason is not identity crisis but their political games.