The terms of the debate over President Trump’s decision to revoke the Deferred Action for Childhood Arrivals program are familiar, as are the terms of the larger conversation about immigration in this country: On one side are hardworking immigrants; on the other are politicians who wrongly claim that these immigrants harm the economic interests of native-born Americans.

As protests broke out across the United States in response to Mr. Trump’s move, reporters and immigrant advocates stressed that the administration’s actions will hurt achievers — people who have graduated from college, people who have bought houses, people who work for high-tech companies.

There is nothing wrong with this story. It’s one that most, if not all, immigrants like to tell about themselves — even if their actual story doesn’t neatly fit the narrative. In fact, as Hannah Arendt pointed out in her essay “We Refugees,” written in 1943 at the height of the 20th century’s refugee crisis, people whose stories fit the narrative least well — the most desperate and the worst-wounded of the immigrants — are especially invested in thinking of themselves as destined for success and, of course, as future loyal citizens.

But something goes awry when this becomes the dominant story told about immigrants in America. This has been happening for a number of years: The good people of America talk about immigrants as hard workers who conscientiously contribute to the economy. (I myself have made it onto a few lists of exemplary immigrant success stories.) In fact, DACA was designed to reward achievement: to qualify for the program, an applicant had to be in school or hold a high school diploma or equivalent, or have been honorably discharged from the armed forces. Those who hadn’t been able or lucky to meet those requirements were apparently deemed unworthy of staying in the country where they had lived since they were children.