The answer to the riddle is not binary. This is not a decision between mental illness or guns. The answer is obviously both.
Let's assume that there is a small percentage of people in the country who are crazy enough to want to kill dozens of people. The question then becomes how easy should it be for them to have access to a gun.
If you have a mentally unstable person living with you, and you leave a gun on the kitchen table and go to work, only to come home and realize this person went out and killed 25 people, you can't just shrug your shoulders and say ... " well it's not the gun's fault, it's the mental disease". Of course it's the mental disease, but you made it incredible easy for this to happen and that's part of question.