It took so long that psychology was recognized because there was no formal approach to the study of behavior. In order to be accepted as a science, psychology had to overcome the influences of religion and astrology for many people believe in these system, in which it cannot be proven.
Moreover, when Wilhelm Wundt set up and organized a laboratory dedicated to the study of human behavior in 1870's in Germany and apply the scientific method to the study of behavior. It was then psychology was accepted. The thing that help him get it recognized was using the specific method called introspection, which is an examination of one's thoughts and feelings and then recording and measuring them to obtain a credible output.