You can just as easily compare suicide rates as you can compare murder rates (which gun control advocates are inclined to do). Of course, you are right about confounding factors, which is why we should be careful about the conclusions we draw. However, I think we can safely conclude that the presence or absence of guns may not be the only factor in determining the suicide rate.
> But you can compare suicide rates between people in the same state who are gun owners and not. They did and it turned out that gun owners have 4 times higher risk of suicide (by any method) than others.
Not really much better than comparing across countries. There is more in common between these two groups, but it still isn't some randomized control trial.
CCW holders have a much lower crime rate than those without. Does that mean that if we take away their permits (and their guns) those same individuals will commit more crime? Probably not.
Likewise, while taking away guns probably will have some influence on the suicide rate, I doubt very much (or not as much as people think).
Not a scientific study, but having known gun owners who were either suicidal or successfully committed suicide, they tend to be the kind of people (men, typically) who carry the weight of the world on their shoulders. The suicidal tendencies come on strong when they feel either like they have failed the people who depend upon them, or that people don't need them anymore. Taking away their guns might keep them from committing suicide long enough for them to get help (or for the feeling to pass) but that is by no means a guarantee. We also cannot ignore the consequences of taking the guns: a psychological loss of agency, and potentially physical loss of security, etc. It's not a simple problem to solve.