Delusions are distorted models in your head about the world around you. Facts, arguments or perceptions will not correct this model. A person with delusions will fit the facts to the model. People with psychoses can entertain delusions, but so do people who believe in conspiracy theories.
A lot of people think antidepressants are worthless. Is psychotherapy better than an antidepressant? There is no evidence for this. It seems to me that antidepressants suffer a disadvantage in our perception as compared to psychotherapy, in that their mechanism of action is quite invisible and not instinctively comprehensible.