Sir, I don't know where you are located, but there is a "Great Debate" mostly by those who live in the respective regions. Over which is better "New York" or "Chicago" Pizza neither of which is quite like I found in Italy, so "Italian American" was a term encompassing the variations on Italian food (and other ethnic foods i.e. "Mexican American" ) so if you have a better way of categorizing common American versions of ethnic dishes, please let me know.
First, I really don't know where this "sir" thing came from. I would prefer you don't use that when you talk to me, if you don't mind.
Second, regarding the Chicago vs New York pizza debate, the question is which one is the best American pizza, neither of which is Italian. And it's really not a question, because the Chicago version is a pie... or maybe a casserole, if you're being generous.
Think about it like this. In America, we have a lot of labels that we use to categorize food. The labels are often based on national origin (e.g., Italian or Chinese) but can also sometimes be a derivative or regional (e.g., Tex-Mex, Southern, or California Cuisine) or something else entirely (e.g., comfort food). The key here is to recognize that these are nothing more than labels.
Often, even when there is a national origin associated with the food, the actual dishes served barely resemble the inspiration. Italian and Chinese restaurants are well known for this, meaning when you go into a Chinese restaurant, you're very likely getting food that is not authentic to China. However, they aren't Italian or Chinese.
Okay. Stay with me here. Last point. In America, we actually have a term that we use when a restaurant is getting closer to its roots: authentic. When an American restaurant does things that are the same as their origin, we call that authentic food. So, when an Italian restaurant actually serves a dish that is the same as in Italy, it could be called an authentic dish. Still not Italian. It's an American dish that is authentic. This is even true when the origin is American. You can make "authentic Cajun" food. Or you can make Jambalya out of a box by Zattaran's, or you can fall somewhere in between. While this would all be American food, but it wouldn't actually be Cajun food, though it may be an authentic representation.