I think you can use the medical comparison to get a point across, but there are obvious flaws in the analogy. I can point to a very specific and detailed pathophysiology for diabetes. I can tell you exactly how that organ is not functioning and what blood glucose testing and medication does.

We can understand the anatomic composition of the brain, but we do not understand the mind. I can't measure your brain chemicals. I can't tell you how the complex interaction of thought, emotion, action, environmental stimuli, and personality influences your subjective experiences. There is no set and readily understood pathophysiology for mental illness. What you are experiencing and what we deem mental illness is a collection of symptoms, in this case indicating a maladaptive pattern of thought, feeling, and action.

We diagnose based on these symptoms. We do not diagnose illnesses like diabetes based solely on symptoms of low and high blood glucose. Doing so would actually indicate a fundamental lack of understanding in the disease, and would likely cause it to be confused with other illnesses that cause similar symptoms. It is presumptuous to say that we know what mechanisms in the brain are malfunctioning and to liken it to failure of another organ.

The concept of a 'chemical imbalance' as the cause of mental illness is a theory. The fact that medication helps people supports that theory. However, caffeine sometimes helps me function, but it is not because I have a caffeine deficiency. Assuming such would be poor science at best and detrimental due to the implications at worst. Use adrenaline instead of caffeine if you want an example of something the body produces naturally. It would be awfully silly if we found that epinephrine can help certain afflictions, assumed that people with those afflictions had an epinephrine deficiency, and left it at that.

The mind is not just a collection of chemicals, and I think this is where spirituality comes in. There is heart and soul in our minds. It is the source of great literature and art. Furthermore, whether a mind is functioning correctly is based just as much (if not more) on situation. Would a child with ADD be considered ill in the days of cavemen? Would a Spartan warrior be challenged by dyslexia? Humans didn't evolve to sit in an office all day. I could envision a society where cynicism was prized and optimism considered disadvantageous. What is "normal" when it comes to our thoughts? You can't summarize that as easily as you can a dysfunction of the pancreas. Whether our brains are "broken" is as subjective as any other interpretation of the human experience.