FWIW, I don't believe that the classic or clinical definitions of "mentally ill" apply to the vast majority of criminals or mass murderers. It's simply too easy to use some comparative analysis of their actions and behaviors with what most people think is "normal" behavior and call any deviation a "mental illness." (Same thinking, BTW, applies to the present and ever popular "diagnosis" of individuals who want to "reassign" themselves to another gender. It's common now to say that these people are "mentally ill" having to live in their biological reality and the "cure" for that "illness" is "gender reassignment" treatments and therapies. But I digress...)
In my opinion, the majority of these violent and anti-social criminal shooters have simply been acculturated or raised and taught that their totally self-centered behavior is normal and acceptable. That is, they act and behave in the way that they were raised in the environments in which they live. Society has failed these individuals by destroying the family unit, seeking to "medicate away" unacceptable behaviors (rather than instill self-discipline through the use of discipline), and created vast swaths of government-controlled living space where the law of the jungle and criminal behavior are the expected norm, where violence is the path to power and success.
It's only when these violent and anti-social criminal shooters step out of the shadows and cross the line into the ever-decreasing areas where such behavior and action are not generally accepted or expected that their actions and behaviors are then "diagnosed" by the progressive-liberal elites and media as "mental illnesses."
In their quest for power and control, progressive-liberals have turned huge areas of the country and masses of its citizens into animals acting on instinct and narcissism, and it's only a problem for them when these people infringe on the prog-libby's imaginary world that they see any problem.