Psychology is a science because it uses the scientific method. Are all practitioners equally adept? No. Is it a primitive science? Yes. So was physics not too long ago. But, I never read that physics was not a science because it was primitive.
Are all, or even most, inquiries reproducible? Probably not. That is as likely to be a function of the discipline's lack of maturity as whether the discipline is a science.
We are still in the stage of uncovering the phenomena in psychology. We discover new forces in psychology every year, such as a newly-found hormone. In physics, we pretty well know what the forces are.
Chemistry is easy because within an element's isotopes each atom is identical throughout the universe. There do not appear to be two identical brains anywhere. We know that if we apply c Calories of heat to a measured cube of i Isotope of e Element at a Altitude in nominal n Atmosphere we get r Result. The mine whence came the atoms is irrelevant as are the miners, the prior owners, etc. But, the history of an individual mind can disrupt a typical cause-effect relationship.
We have come to some general conclusions: most psychiatric disorders have a somatic component, malleability of some characteristics is limited, there is a strong cause-effect relationship between childhood abuse and an adult's mental illnesses, and a few thousand more. Identical twin studies help, but there are few subjects available. Heritability is a question. Interaction between toxins and brain cells and then the rest of the body is poorly understood.
Diagnosis by reported or observed symptoms is the best we have in some cases. And, individual diagnosticians can go very far off track. I was supervising a neuropsychologist who was himself overseeing a new PhD's residency when I encountered a disturbing issue. A patient was diagnosed with Narcissistic Personality Disorder, but something wasn't quite right. The patient was retired from the US military and the neuropsych had pulled his military medical records before seeing him. He asked the patient to describe his career, and knew immediately he was displaying grandiosity. An enlisted member simply didn't have the kind of career the patient described.
The neuropsych had tested the patient's IQ using Stanford Benet and concluded it was about 145. That is far too high for the patient to have had any confidence in pulling off his claims. I went into the Defense Department's master database and found that the patient had retired as an officer; the local database indicated the patient had retired in 1995 in an enlisted rank that had been abolished in 1975. In somatic medicine that is called treating the lab report instead of the patient. Every other reported "symptom" was confirmation bias.