Your limited view of mankind is blinding you to the truth. You are like a child that has never been outside but has a window which he can see the sky, and since there is a tree outside his window he imagines that everyone sees the sky through leaves.
The truth is much larger then that. The truth is that we are inherently violent creatures. Our culture is not mentally ill. It is just a reflection of our nature. We come from creatures that had to kill to survive. We are still that creature, and when the correct stimuli is presented, we fall back on that nature and commit violence. It turns out that the things that cause us to get violent are extremely common, to the point that almost everyone encounters it daily. We are all going to commit violence at some point. You can not remove it altogether. So, our goals have to be twofold, one to control the output of that violence to make it either harmless or productive, and to limit the damage it can do on those occasions when it is uncontrolled.
We do a reasonably good job at the first goal, most of the time when people get violent the effects are minor. It is the second goal that we are failing at badly, and guns is just one small, but very visible, part of that.