The Behaviorist school at least tries to quantify behavior in statistical terms, thereby rendering "normal" as an objective value. The danger there is that in doing so, they reduce their patients to little more than statistical abstractions -- dehumanized standard deviations or analyses of variance.
So while psychology isn't the "hard" science that math is, it can be described scientifically, if that evolves to the patient's benefit. However, I doubt that it does.
Behavioral psychology is the only psychology that is a science.
That doesn’t mean that patients are reduced conceptually to automatons, or that behavioral conditioning is a good idea.
It just means that general truths can be inductively derived from psychology experiments.
Take, for instance, random reinforcement. It turns pigeons into maniacal key tappers. Apply it to child-raising methods. Voila! Various maladies of the adult.