One is ither an American or an Indian. One can’t be both.
I see the “Indian” part as a descriptor of what kind of cultural heritage and childhood background the now-current American has.
I agree with you whole heartedly. However United States has this tradition of categorizing people such as White-Americans, Black-Americans, Native-Americans, and that continues into calling even 2nd & 3rd generation Americans with a prefix such as Italian-Americans, Hispanic-Americans etc.
In my honest opinion, when one becomes a US citizen, one takes the oath to be a loyal citizen of US and then becomes simply an “American”. The sooner we stop classifying people into categories, the better.