This was evident in both the Facebook page and the response to it by Facebook’s management, who, despite the site’s anti-bullying policy, initially refused to remove it on grounds that it did not target named individuals. “Families Against Autistic Shooters” remained accessible until last Monday, by which time escalating media attention and a petition on Change.org with nearly 5,000 signatures embarrassed administrators into action. For the time it was viewable, the page stigmatized a population far more likely to be attacked than to attack, far less likely to receive justice when injured, and far more likely to be misunderstood. That devaluation of autistic lives is far deeper than any autistic devaluation of neurotypical lives.

Such prejudice arises in part from confusion about autism, which manifests in a multiplicity of symptoms, making generalizations difficult. Some people with autism cannot easily guess what other people are thinking, and therefore act without socially appropriate nuance. This perplexity is often conflated, unfairly, with lack of emotional empathy or even unkindness. Autistic people run the same gamut as other people: Some are kinder than others. Some find social interaction extremely taxing; others evince joy in trusted friends and family. Whatever anyone’s particular constellation of symptoms may be, however, autism is not associated with brutality. Failing to intuit certain aspects of other people’s inner experience does not equate to disdain for human life.

The wish to hurt others is tied not to autism but to psychopathy, which manifests in a deficiency or absence of empathy and remorse. Some autistic people may not recognize why they cause distress; psychopaths don’t care that they cause distress. Autistic people may see the world from a singular, personal perspective; psychopaths are often cunning manipulators who act according to perceived self-interest without regard for the destruction they cause. Psychopathy seems to have coincided with autism in the cases of Mr. Harper-Mercer at Umpqua and Adam Lanza at Newtown, Conn. Psychopathy apparently coincided with depression and grandiosity in the cases of Eric Harris and Dylan Klebold at Columbine and Elliot O. Rodger at Isla Vista, Calif. Psychopathy almost certainly coincided with schizophrenia in the cases of James Holmes in Aurora, Colo., and Jared Loughner in Tucson.

You can categorize such people as having a common madness only if your criterion for madness is their behavior itself. To say that you’d have to be crazy to shoot up a school is not the same as saying that crazy people are predisposed to kill. Fewer than 5 percent of gun crimes are committed by people with mental illness; fewer than 5 percent of people with mental illnesses commit violent crimes.

Tarring the autistic community in this manner — like presuming that most black people are thieves or that most Muslims are terrorists — is an insidious form of profiling. It exacerbates the tendency for people with autism to be excluded, teased and assaulted in childhood and adulthood.