What's it mean to be Greek?

  For the recent assignment of my English class I had to read an excerpt from "Hunger of Memory" by Richard Rodriquez.  In the story Rodriquez recounts growing in a Mexican-American household, and his initial struggles with learning English.  Spanish was his first language but as he grew older and overcame his struggles with English, English became his primary language.  He was still able to understand Spanish but he could not speak it fluently. 
    His childhood is very similar to my own.  I was born in Greece and came to the US with my family when I was about 6.  I initially spoke Greek but I'm no longer fluent, what remains of the language are bits and pieces.  There are early home videos of my brother and I speaking in Greek, and it's like watching completely different people.  Now I can recount certain words, but like the author I can't put together a coherent sentence.  If someone were to ask me "How do you say this or that in Greek?" I would not be able to tell them.  
     When I'm with my parents I can almost follow conversations in Greek between my Mom and Dad.  My Mom can ask me a question in Greek and I will respond in English. When friends are over and witness these exchanges, they thinks it's the weirdest thing.
      And it's only the Greek that my parents speak that I can understand.  I once went to the Embassy in Houston and the lady working there initially spoke to me in a kind of 'rapid fire' Greek.  To me it sounded as if she was speaking complete gibberish.  I could only shake my head in response and then see a look of disappointment in her face.  I guess my parents maybe speak a different or slower dialect of Greek.
       Such encounters often make me feel guilty.  In a blog from a fellow classmate, The Clash of Culture, it says that language often is the root of a culture.  So does my ignorance of the Greek language exclude me from being a part of Greek culture?  Or does simply my blood or inheritance qualify me as a Greek?   These questions often resurface when I see distant relatives or when friends ask me to translate something from English to Greek.
     But in his essay, Rodriquez goes on to say that though some intimacy is lost between him and his family there is some that remains.  That intimacy "is not created by a particular language; it is created by intimates."  So what I should be concerned with is not whether I identify as a Greek person but rather if I can still identify with my immediate Greek family.  That is the only culture I should be concerned with, one that is a cross between Greek and American.