I live in Arizona, where there a lot of first and second generation born in America, mostly from Mexico. And, like everything that you are born with, and can't ever change, people have mixed feelings about not really "being American". But they are, as I am.
I know nothing about Mexico, but I have lived in Arizona long enough to know that it is a place that many people want to leave, and come to America. And my research on southern Italy, where my grandfather Lorenzo Scinto was born, says that it was the same kind of place. My Italian family lived in a world of grinding poverty. America was a place of opportunity, a place to dream of.
The Scintos settled in an Italian neighborhood in Chicago. Lorenzo (who went by the name of John), attended school there. And while a six-grade education doesn't seem like much, it was the highest education that anyone in his family had ever achieved.
I never knew my grandfather, he died when I was a baby. My understanding is that he spoke English without an Italian accent, in spite of the fact that his parents never learned English. I am told that the only way you knew that he was Italian is that he "talked with his hands", moving them around all of the time. A stereotypical Italian behavior, I understand.
I don't know if my Italian ancestors dreamed of a better life for their descendants. Maybe they didn't dare to dream. But I am living in the world that they provided for me. I am an American.