Lets look at the argument. First he states that the spending on drugs has increased rapidly in the last 10 years as have the number of people diagnosed.
Then the arguments:
In the past 50 years, the number of people diagnosed with mental illness has gone up. If we could cure mental illness, we would expect it to go the other way.
The problem with this argument is that it can be applied to many forms of cancer or other illnesses which have also gone up in prevalence in the past 50 years and does not account for better tools being available for diagnosis and treatment today.
Second argument
psychiatry has yet to conclusively prove that a single mental illness has a physical cause or a genetic origin
and no two species have been conclusively observed to evolve into each other. There is plenty of contrary evidence for instance: https://www.nih.gov/news-events/nih-research-matters/common-genetic-factors-found-5-mental-disorders
Then there is some quote-mining. Quotes that indicate that no single cause or condition can be identified as having a 1:1 correlate with a single mental illness is used to support the wider claim that mental illnesses do not have clear physical and chemical correlates. This is right out of the scientology playbook, wonder if we will hear about how cruel certain treatments are in a moment?
The case of schizophrenia is discussed. It is brought up we don't know the precise cause of schizophrenia (true) or how it is best treated (true). It is begrudgingly brought up twin studies demonstrate there are changes in the brain in patients with schizophrenia compared to their normal twin (which is damn good evidence those changes are related to schizophrenia), however he pulls out the explanation that these changes are CAUSED by giving the schizophrenia twin drugs. No citation is provided for this claim. The theory is, then, that the brains are initially equal but one have schizophrenia. Then that person is administered "brain-altering drugs" which changes his brain so it looks like the changes in the brain correlates with schizophrenia. This claim does not take into account the observation schizophrenia has an obvious inheritable component to it.