It seems a matter of common sense to think that 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? Mental illness is a medical matter, not a matter for common sense pop psychology to resolve.
Looked at in strict medical terms, mentally ill people do not make up the majority of mass shooters and about 3% of violent criminals are mentally ill. 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 certainly a matter of concern, but mass shootings and gun violence are not, if one looks at the data, primarily a mental health issue. While the mentally ill commit some gun violence, focusing on mental illness as a 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—engaging in a mass shooting is clear evidence of mental illness since a sane person would not do this. While this does have some appeal, expanding the scope of mental illness to automatically include those who engage in mass shootings as mentally ill would be problematic.
One obvious concern is that soldiers and police who have engaged in shootings with multiple casualties would thus be classified as mentally ill. In war, soldiers regularly kill large numbers of people, including the innocent and unarmed. Yet they are not classified as mentally ill simply because they use violence as a tool to achieve their ends (or the ends of others).
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 are sent to kill to address 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 as 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 seem to eliminate the notion of evil. If people do bad 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 just 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 certainly be challenging. After all, if a white supremacist kills people with guns because he is mentally ill, then the same would apply to a member of ISIS who kills people with guns or bombs. 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 crimes—it is interesting to compare the rhetoric used by the same person 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.
In light of the above discussion, the mental illness explanation for mass shootings (and gun violence) does not provide an adequate account. While seriously addressing mental illness would be laudable, it would not eliminate mass shootings and would have an insignificant impact on violence (other than self-inflicted violence). This is not to say that mental illness should not be addressed—it should! But to give speeches about mental illness to explain gun violence is an error and a distraction from addressing the significant causes of gun violence.