Think of the biggest possible insult to a person with whom you disagree politically. How about "you don't belong here?" That's the essence of what is being said when citizenship is denied to people who otherwise are full-time permanent residents of the country.
This is not about undocumented immigrants; through our history the non-citizen card has been played many times against many groups of people. Law professor Amanda Frost documents the history in her book You Are Not American: Citizenship Stripping from Dred Scott to the Dreamers.
The author leads us through the tales of people marginalized through the years.