Personal opinion-
I think the reason so many providers cannot wrap their heads around psych patients and their problems is because there is so little we can actually do for them. As EMS providers, we want to fix things- ASAP- and there is little we can do for a truly disturbed individual. We cannot "see" the problem, so often times we minimize or even dismiss it's impact or importance. There can be a chemical imbalance, some sort of emotional trauma, or an extended history of personal problems that lead a person to the point in time were we encounter them. If someone is having chest pain, we can "cure' that pain with one pill. If someone is depressed, all we can offer is a sympathetic ear. Sure, if they are exhibiting symptoms from an OD or physical trauma, we know how to treat that. Therapy, counseling, trial and error with various treatments and medications- it's often a long and difficult process to get a person on solid emotional ground, and that process usually includes multiple trials and errors of medication combinations; there is no quick fix.
As for suicide in particular- we all know that a legit attempt makes folks far more likely to try again- and eventually succeed. I've had folks with extensive psych histories finally succeed after many half-assed attempts. I also had one guy who immediately after receiving a diagnosis of cancer(unknown type or stage) go from his doctor's office to the high rise building he worked as a building engineer. When he arrived at work, he made an offhand comment to a coworker about receiving the diagnosis, proceeded to the roof of the building and jumped 40 stories to his death. He went from a cancer diagnosis to dead in a matter of a couple hours. (That one was particularly disturbing)
Point is, everyone has a different threshold and tolerance for physical as well as emotional pain. A problem that may seem inconsequential to most folks can completely overwhelm another person's ability to cope. As a provider we need to look at psychiatric patients through their eyes- as much as possible. No, we should not begin talking to someone's visual hallucinations, but at least try to understand their stated concerns. Even with seriously delusional folks, there are usually nuggets of truth embedded in their rantings. Yes, many of our suicide calls are not serious. A teen girl takes 4 Motrin because she is upset her boyfriend dumped her. Is she serious about her desire to die? No, but she does need perspective, which is something we can give- at least until counseling can take over.