The only reason I'm a citizen of American is because of the 14th Amendment of the Constitution:
Section 1.
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
That is, the law of the U.S. defines my status as a citizen of the U.S. by virtue of my being born here.
Still, there are four other ways to become a citizen of the U.S.
by naturalization
by marriage
through parents
through the military
These pathways are all outlined in various laws.
Again, the status of immigrants who are now citizens is determined by law.
I said earlier that "the 'We support a legal path to citizenship for immigrants that go through the proper channels' people do not, in fact, support a legal path to citizenship for them". That is, Republicans generally refused to grant citizenship to immigrants by passing the DREAM Act. In their inability to govern, they did not pass a law.
You make it seem as if citizenship is an inherent characteristic of being born in the U.S. It is not. Repeal the 14th Amendment, and birthright citizenship goes away. Change the immigration laws, and lesser or greater numbers of immigrants can be granted citizenship. You're right, "They are not citizens of America." But they could have been (and could be) at the stroke of pen. It is the law that determines citizenship. While I'm both an American citizen and identify as American, dreamers only identify as American. It's only because of xenophobia that dreamers are not citizens.