Why do Mexicans say Mexican Americans aren’t Mexican? Isn’t that just confusión nationality and ethnicity?

I'm Mexican American and recently stayed in hostels while traveling around Europe. I met people from Mexico, and it felt kind of weird like they saw themselves as fully Mexican and me as just American. I could really feel the difference in culture between us.

At the same time, l've lived in parts of the U.S. that are like 90% white or 90% non-Mexican, where I'm clearly seen as having Mexican roots based on how I look and my background. So it's interesting to feel "Mexican" in one place and then not in another.

So I'm curious:

Do people in Mexico generally see it this way?

Is it more about culture than ethnicity?

Or is there some level of gatekeeping?