Hey Clemency and Copy Cat,
I think it's somewhat confused to talk about an entire discipline, either psychology or psychiatry, as being a science or pseudoscience. Instead, it's much clearer to talk about certain claims, explanations or theories and ask if they're scientific. As Copy Cat correctly noted, a theory is scientific if and only if it makes claims that can be tested. However, there's an extra criterion that CC missed which is falsifiability. The claim in question must in principle be falsifiable in the sense that it must be possible for investigators to show that claim is not true.
With that said, many of the objections people make to psychology and psychiatry are usually in regards to certain normative practices that they cannot justify with evidence because the normative practices are presupposed and antecede any kind of research. For example, the Diagnostical Statistical Manual of Mental Health and Behaviour Disorders (DSM) is a system of classification which is used to identify certain populations. It also stipulates the criteria for the use of certain concepts (i.e. Major Depressive Disorder, Bipolar Disorder, Anorexia Nervosa, etc). But there's nothing researchers can do to justify their system of classification. It's not handed down by God or Reason-with-a-capital-R. It's normative in the sense that it organizes researchers and clinicians around a shared vocabulary so that they can go out in the world and do research and communicate their results to each other.
Of course, this opens up the DSM to alot of criticism because of how arbitrary it seems. Homosexuality was a mental disorder now it's not but Masochism is. Onanism was a mental disorder now it's not but juvenile delinquency (conduct disorder) is. Hysteria was a mental disorder now it's not but transgenderism is (gender identity disorder). You can see why people shake their heads at what's going on with the APA/CPA.
The same follows for concepts researchers use like "mental illness". It's not as if the grammar of psychology/psychiatry is handed down by God or Reason-with-a-capital-R, it comes from certain normative practices which can't be justified by research because the meaning of concepts is logically presupposed by researchers (if you doubt this you can try and do research without knowing the meaning of words in our language. If you get anywhere with this please let me know. I'll be curious to know how you did it

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Take care guys.