Birtherism was the complaint of cranks from the beginning, and it should have died in April 2011, when, in response to Mr. Trump’s taunting, President Obama obtained and released a copy of his original birth certificate from the archives, which proved he was born in Honolulu.

The theory lived on for several more years, but not because there was evidence for it. Empirical evidence was never birtherism’s appeal. What made it attractive, what made it so hard for its exponents to relinquish it, was their hatred of Barack Obama. His fans often claimed such hatred was motivated by racism, but every recent president has been hated by large numbers of people.

Birtherism and the insistence that Mr. Trump is a racist are very different sorts of crotchets. But they have one thing in common. Devotees of both fully believe that once the truth is acknowledged, everything must change: The objects of their hatred will have to go away and never return. Hence the birthers’ preposterous theories about how Mr. Obama’s birth certificate was forged.