But, as Asne Seierstad writes in “One of Us,” her book on Mr. Breivik, two court-appointed forensic psychiatrists interpreted his lack of empathy another way: as a symptom of paranoid schizophrenia, which in Norway meant Mr. Breivik would be sent to a psychiatric hospital rather than to prison. The diagnosis was made despite the fact that Mr. Breivik himself described the mass murder he committed as a political act, a deliberate slaughter he willfully executed in accordance with his beliefs. As in Mr. Gendron’s case, these beliefs were not Mr. Breivik’s alone. They were shared by some members of the Progress Party, an anti-Muslim party to which Mr. Breivik had belonged. (Its leaders condemned his actions.) A second psychiatric evaluation subsequently concluded that while Mr. Breivik exhibited signs of dissocial personality disorder and “narcissistic traits,” he was not psychotic, clearing the way for his trial and conviction.

As Mr. Breivik’s case shows, determining who should be classified as a mentally ill offender is not easy, not only for diagnostic reasons but also for moral and political ones. In his book “Hatred: The Psychological Descent Into Violence,” the psychiatrist Willard Gaylin argues that the ubiquity of psychodynamic interpretations of destructive violence risks trivializing it.

To illustrate the danger, Dr. Gaylin cited the response of Cardinal Bernard Francis Law, the archbishop of Boston, during the deposition for the trial of John J. Geoghan, a Catholic priest who was found guilty of groping a 10-year-old boy and accused of raping and molesting more than 130 children, abuses his superiors knew about for decades. “I viewed this as a pathology, as a psychological pathology, as an illness,” said Cardinal Law about such allegations. It was a striking departure from the kind of rhetoric the church typically used when condemning conduct it regarded as immoral, like homosexuality and abortion. It also underscored what can happen in a culture “where nothing is either wrong or right, only sick or healthy,” Dr. Gaylin contends, “where nothing is deemed punishable, only treatable.” To confront violent hatred, we need to be able to name and identify it as evil, Dr. Gaylin maintains, an imperative that therapeutic language can stunt. “If all aberrant behavior were sick, there would no longer be any room for judgment,” he argues.

But acknowledging the role that mental health problems can play in hate crimes does not require downplaying their perniciousness or diverting attention from the inflammatory language and ideas that can fuel their rise. Too often in America, there seems to exist a false binary: medical problems versus political ones. The truth is that it’s often impossible to disentangle the internal experience of mental illness from the external social and political forces shaping the world. And the mentally ill are no more immune to these forces than the rest of society. One reason the rhetoric of figures like Mr. Carlson is so dangerous is that it can seep into the culture and eventually help trigger an angry, mentally unstable individual to act violently. It may fuel stochastic terrorism — violence inspired by incendiary rhetoric whose eruption is predictable even if the specific details are not.

In 2019, a gunman in El Paso, Tex., opened fire at a Walmart, killing 23 people, many of them Latinos. The alleged perpetrator, a 21-year-old white man named Patrick Crusius, who has pleaded not guilty, is, according to his lawyers, psychotic, but his choice of targets hardly seemed random. Before committing the mass shooting, investigators believe he posted a manifesto on 8chan decrying the “Hispanic invasion” of America, a sentiment voiced by a growing chorus of xenophobic figures on the right in recent years, most notably Donald Trump.

Edward Dunbar, a professor of psychology at the University of California, Los Angeles, who researches bias-motivated crimes, does not find it surprising that during the pandemic, as anti-Asian rhetoric swirled through public discourse — not least thanks to Mr. Trump, who repeatedly referred to Covid-19 as the “Chinese virus” and “kung flu” — some people with mental health disorders acted on it. As Professor Dunbar noted, one thing that can cause hate crimes to surge is when public leaders demonize a group, effectively sending society a message that there will be no social cost to harming its members. No one should be shocked when individuals who are impulse disturbed or suffer from persecutory delusions end up lashing out, Professor Dunbar said, particularly when the demonized group is perceived to be successful — an assumption that has long been made about Asian Americans — by individuals whose mental health struggles may be compounded by homelessness or poverty. “As with previous waves of antisemitism, the resentment at Asians is directed toward those who’ve done well and are doing better than you,” Professor Dunbar explained.

In this respect, it’s worth noting that most of the mentally ill people who were arrested for assaulting Asians in New York City during the pandemic weren’t just emotionally disturbed. Many were also destitute — people like Martial Simon, a Haitian American with schizophrenia who in recent years had been spotted at a soup kitchen mumbling angrily to himself. Much of his fury was directed at doctors and the medical establishment, owing to the fact that, again and again, Mr. Simon had been hospitalized and then abruptly discharged before he felt stable.