Psychological reasons cited include

the placebo effect
the will to believe
self-serving biases that help maintain self-esteem and promote harmonious social functioning
demand characteristics - the obligation to respond in kind when someone does them a good turn[
post hoc, ergo propter hoc fallacy ("after this, therefore because of this"; the basis of most superstitious beliefs)
psychological distortion, such as confirmation bias and cognitive dissonance (inability to respond to criticism of alternative medicine in order to reduce one's cognitive dissonance)
patients' unpleasant personal experiences with hospitals, doctors, and nurses and perceptions of rude, cold interpersonal interactions.
emotionally positive and psychologically affirming experiences with alternative practitioners.
painful, unpleasant, and sometimes dangerous side effects of biomedical treatments. Treatments for severe diseases such as cancer and HIV infection have well-known, significant side effects. Even low-risk medications such as antibiotics can potentially cause life-threatening anaphylactic reactions in a very few individuals. More commonly, many medications may cause minor but bothersome symptoms such as cough or upset stomach