I totally understand what OP is saying. I had the same exact feeling about this as well. Not only is the identification and quantification (measurement) of the illness is limited to what the person/patient can describe it is also limited to what the therapist/doctor can get from the patient. If the doctor lacks certain knowledge about the illness and the problems that the patient is facing, there is sure to be some missed diagnosis at least. The diagnosis can vary widely depending on various factors (from understanding, empathy, trust, descriptive language ability, ability to bridge differences between them, and even the emotions) But there seems to be a procedure to minimize all those factors in the diagnosis process.

During the patient intake, they would discard many of those factors and write down the most relevant info and does the actual diagnosis only after gathering everything necessary (you do not get diagnosed right away). With training and experience, the professionals would know how to draw out the information from not just description but also body language. That's why trust, empathy and being completely truthful is very important. It is not something you can learn just from reading a book like a manual which is why some professionals can be better than the other. It is also very important to pick the professional that matches the patient's criteria. ( Adolescent or adult, learning disability or anxiety, etc)