One of my favorite holidays in America is Thanksgiving. We are all thankful that we have one another, and so God has blessed us as a family.
My family includes people from Asia (my wife is Chinese Indonesian), Africa (my daughter-in-law is from Zimbabwe), Germany (my mom was born in Germany), Haiti (my daughter's partner grew up in Haiti) and I am for the most part "fully American" (as in except for the rare German meal to remind me of my mother's cooking, we don't celebrate German traditions, holidays, etc., but rather we enjoy the diversity of cultures that have blended into what is in my mind, the best culture in the world, American. America has "appropriated" the best of so many other cultures and made them "American".
And so, on Thanksgiving Day the side dishes at our table speak to where our family histories lie (including our "special" family cranberry Jello recipe that came off a box of Jello in the 1950s). Asian dishes, African dishes, Caribbean dishes, and of course that most American food... Turkey.
So, what does it mean to be "American"?
In our family, it means simply that you are committed to the core values that define our country including the belief in individual unalienable human rights granted by a Creator to all humans. That you are committed to the idea of an economic system that allocates goods and services through the marketplace but maintains a social safety net for those unable to help themselves. It means tolerating those who hold beliefs you reject, since without tolerance, individual liberty does not exist. It means promoting integration at the racial, cultural, social, biological, and political level... the so called "melting pot", where immigrants from all over the world embrace their new nation but retain a part of what they loved most about the culture and traditions from which where they have come.
Like any "soup" every new ingredient added to the soup, changes its flavor, it makes the soup more robust. It is still "American" soup, just better.
Having someone remark that you are "becoming" American does involve embracing American traditions and not every immigrant that comes to America does that, but it also means bringing along some of your traditions including your food culture and adding it to "the table". My guess is most Americans do not have "fried rice" for Thanksgiving (they have no idea what they are missing or a Zimbabwe dish of stewed vegetables to die for). How about adding some Mojo to your Turkey to make moister and more flavorful.
In other words, like the differences between men and women, which make life interesting, the differences between Americans from different cultures makes being American interesting.
Anyways, I guess you have your experience as an immigrant, but in our family, we embrace "differences" and at the same time common values. I think that is true of most Americans. Even living in the Midwest without nearly the diversity of California, New York City, or South Florida, we found people were excited to meet and break bread with people from other parts of the world.
Regarding the question of when does someone become "truly American", I think that occurs when you trace you core beliefs regarding the values that should govern a society to the words contained in the Declaration of Independence, the Constitution, and the great speeches of the past like the Gettysburg Address, JFK inaugural speech, and MLK's vision speech. At that moment, you have become "American".
