"It seems like mental illness and frustrations with society"

And of course it is, but mental illness is really only a definitional claim. When you say that someone is mentally ill, all that really means is they meet criteria that we've decided makes them fit to be consider mentally ill. One of these criteria could very easily be "murderous intent." Of course there are underlying problems that lead to the development of these issues in the first place. But mental illness and school shootings don't have to necessarily directly correlate.

Mental illness and frustrations are one thing of course. The "outsider" feeling that these individuals experience is the catalyst for acting out of some sort, but it can manifest itself in very different ways. Shooting a bunch of people and receiving notoriety for it is HUGELY appealing to people who see themselves as outcasts of an unjust society. This allows them to become a martyr of sorts for anyone who feels the same way, and they find comfort and validation in knowing that there are others who would look up to them for committing such acts.

This is of course, all within the realm of mental illness, but simply calling it ill or disordered doesn't begin to address a solution. Even the actions of the mentally ill follow some sort of logic, and while it may stem from jealousy/frustration/mental illness, the way that they respond to these negative stimuli is something not too much different from the way humans tend to rationalize things, albeit in a more exaggerated way.