How come there is no general health doctor that is not allowed to prescribe prescriptions? like how there are psychiatrists (allowed to prescribe prescriptions) and psychologists (not allowed to prescribe prescriptions)?

Psychiatrists : Psychiatrists have gone to medical school just like surgeons and family practice doctors. That education has given them the knowledge of physiology and pharmacology needed to safely prescribe medications. Psychologists have not gone to medical school. They typically have a college degree in psychology - possibly a master's or phd, but do not have a medical degree and so cannot legally prescribe medications.

Medical School: One must attend and graduate from medical school and then pass a series of examinations before being allowed to obtain a license to practice medicine. Psychologists do not attend medical school. Hope that helps.

Medical training: All physicians (including psychiatrists, who are physicians) go through extensive medical training which includes the comprehensive effects of medications on human physiology, consciousness, and behavior. They are supervised in learning to prescribe safely & effectively. Psychologist training concentrates on other areas, with some possible overlap in neurophysiology, etc. See comment below.