The national debate appears to be stuck on a guns vs. mental illness dichotomy, with both sides insisting their positions are self-evidently true.
There is a third position that may be helpful: chaos theory, according to which the behavior of objects is not always predictable. If we run an experiment 3 times, we will probably get the same results. But if we run it 3 million times, we will notice slight deviations. No matter how predictably objects appear to obey the laws of physics, there are always results we can't explain.
If we reflect on our behavior, we may see that it, too, is not always predictable. We do things on a whim, or in response to stimuli, that make no sense. People who may or may not be mentally ill do things that appear sick to the rest of us, although they were not demonstrably ill prior to the event. Realizing that, if we make weapons generally available, some of those events will involve those weapons. If weapons are less available, there will be fewer incidents.