One the face of it, it is reasonable to think a mass shooter must have “something wrong” with them. Well-adjusted, moral people do not engage in mass murder. But are mass shooters mentally ill? The nature of mental illness is a medical matter, not a matter for common sense pop psychology or philosophers to resolve. But critical thinking can be applied to the claim that mass shootings are caused by mental illness.
Using the strict medical definition, mentally ill people do not make up the majority of mass shooters and about 3% of violent criminals are mentally ill. Research consistently shows that the mentally ill are more likely to be victims of violence rather than perpetrators. Violence on the part of the mentally ill tends to be self-directed rather than directed at others.
Self-injury is a matter of concern, but mass shootings and gun violence are not primarily a mental health issue. While the mentally ill commit some gun violence, focusing on mental illness as the primary means to reduce gun violence would be an error, except to address cases of self-harm.
It could be objected that the definition of mental illness used above is too narrow and that engaging in a mass shooting is evidence of mental illness because a sane person would not do such a thing. While this has some appeal, expanding the scope of mental illness to automatically include those who engage in mass shootings would be problematic.
One obvious concern is that soldiers and police could thus be classified as mentally ill simply by being involved in shootings on par with a mass shooting. It could be countered that soldiers and the police (usually) use violence legally and rationally while mass shooters and people engaging in other gun violence do not. While it is true that mass shootings and gun violence are illegal, mass shooters do often act from grievances and ideology, just as soldiers and police are sent to kill over grievances and in accord with an ideology. As such, killing people for these reasons does not make someone mentally ill, unless we want to classify combat veterans and some police officers as automatically mentally ill. As far as the legal aspect is concerned, breaking the law hardly seems to show someone is mentally ill, otherwise all criminals would be insane and thus would always succeed in the insanity defense.
A second concern is that assuming mass shooters are mentally ill would eliminate the role of evil. If people do mass shooting things because of mental illness, then they are not evil in a morally meaningful sense. While this could be true, such an approach to evil would need to be applied consistently and not just to mass shootings. So, for example, when terrorists crash planes into buildings or blow up a wedding, they are suffering from mental illness and are not evil. One could attempt to work out accounts of ethics and mental illness that put the blame for gun violence on mental illness while putting the blame for terrorism on evil, but this would be challenging. After all, if a white supremacist kills people because he is mentally ill, then the same would apply to a member of ISIS. Interesting enough, while Republicans and the NRA rush to blame mass shootings on mental illness, they do not do the same for terrorism or other crime and it is interesting to compare the rhetoric used by the same pundit or politicians to describe these situations. This is not to say that a case cannot be made for eliminating the concept of evil in favor of the concept of mental illness, but this must be done in a principled manner and applied consistently.
Considering the above discussion, the mental illness explanation for mass shootings (and gun violence) is not adequate. While seriously addressing mental illness would be laudable, it would not eliminate mass shootings and would have an insignificant impact on most violence (other than self-inflicted violence). This is not to say that mental illness should not be addressed, it absolutely should. But claiming mental illness explains gun violence is an error and a distraction from addressing the causes of gun violence.