So, do you want people to actually kill themselves, or attempt and get help? Because the presence or absence of a gun in the home is very often the difference between those two scenarios.
Really, it's the same math as "But you can kill someone WITHOUT A GUN": having a gun around changes the impact of someone's suicidal/homicidal intent. People are going to get angry or depressed, but guns are really powerful at turning those (temporary) states into PERMANENT deaths.
This is a harm reduction way of looking at the issue, not a moral one, but less harm is something that I imagine we all want.