Well honestly I think they do usually have mental health problems, but I think it combines with something more than that.

My biological father bought firearms just for the sake of the "cool factor" (not for hunting or self-defense) and also wound up making death threats and getting restraining orders against him and his guns taken away.

He had mental health problems, but he was also a very nasty, vindictive person who felt the world owed him and that he had the right to treat people however he wanted without consequences.

In the end his mental health problems made him crazy enough to aggressively act out his nasty beliefs that stemmed from from a cruel and entitled personality. It was like it all combined to form a nightmare of a person.

On the other hand, I've been even more psychotic than my father ever was on multiple occasions, and I went on a mission to save all the homeless people in California, guided by higher powers, of course.

I think we'd be kidding ourselves to think that people who go on suicidal, homicidal rampages against strangers don't have mental health problems, but there is definitely more to it than that.