This could easily be 'why do people hate and distrust physicians?' because I think you will that that are
many many people who believe that doctors are evil, they are arrogant, they put their own interests before those of their patients, suppress the evidence for treehugging, reiki and homeopathy, created HIV to kill black people, are witholding the cure for cancer, advocate useless vaccinations to line the coffers of pharma and hide the truth that they cause autism and death (or mental ******ation according to Michele Bachman), and that we are all corrupted by our own greed and opulence and like nothing better than lording our power over sick people. You will find people who believe that doctors cause more problems than they treat (read Medical Nemesis), people who believe that obstetrics is a travesty and obstetricians have no role in the natural process of childbirth, that neonatology is a travesty, and I could go on... It is unsurprising that a profession that is so often regarded as saviors, can so easily be portrayed as abusers!
I have met these people and they are scary!
It is valid for medical students to have these concerns about psychiatry, but if you really care what people think about you maybe medicine isn't the career for you period. The majority of the US population no longer believe physicians are highly trustworthy (nurses narrowly beat doctors in the trust polls). Politicians are always attacking the medical profession.
Psychiatry has a long history of abuse (as has medicine) with individuals incarcerated for no clinical reason receiving barbaric treatments such as lobotomies and unevidenced based treatments like bowel resections, blood transfusions, tooth removal, insulin comas, extremely high doses of unmodified ECT and there are a vast number of competing theories to explain psychopathology (cognitive, behavioral, biological, psychodynamic, existential, social realist, social constructivist, nihilistic, humanistic etc) which historically has divided psychiatry. Many of these problems are in the past today.
Unfortunately there is still a lot of misinformation about mental illness, which some people see as purely moral, spiritual, or social in origin (some of it is, most of it isn't) and so the medical formulation and treatment of 'deviant behavior' often is very emotive.
Psychiatry is not a science, but neither is medicine. It is however informed by the scientific method - we make observations, develop hypotheses based on those observations, test those hypotheses, collect the results and interpret and make inferences about the meanings of those results. That is what science is. psychiatry is increasingly evidence based and we use epidemiological methods to try and better classify and understand the causes of mental illness. Randomized controlled trials and meta-analyses are used to evaluate the treatments. There is a burgeoning literature on the genetics of severe mental disorders such as schizophrenia (for example we now know ~1% of schizophrenia cases can be explained by large chromosomal microdeletions) and cognitive neuroscience is helping us understand the neural basis of emotion and cognition both normal and abnormal.
Now we are not as advanced in our understanding of pathology, or clinical treatments as epidemiology, but we are far ahead of most of chronic disease management, pediatrics, obstetrics, and many surgical specialties in terms of evidence base for clinical practice.
Most people don't hate psychiatrists, but there are those that do. Then again there are those who hate all physicians in general.