Caveat: this is not a fully developed thesis, just some notes for later.
First, there is the problem of the scope of “psychology”. There are things within the scope of that word which are unquestionably “science”, particularly those matters which pertain to physiology. But the word has such a great scope that there are many things which cannot reasonably be called scientific.
Second, there is the question of what can be captured by scientific methodology. Isolating and test for a particularly variable (some agent of action) is difficult enough when we are considering matters involving the functioning of the human body.
The question becomes more complex when we consider various systems of the human body — such as the interactions between various parts of the nervous system.
When it comes to gross-level human experiences the sheer complexity of the nervous system is likely beyond any ability to model.
When it comes to human behaviors, it is unquestioned that environment has effect upon observable human experience covered by “psychology”. The complexity of the environment when coupled with the complexity of physiology makes “scientific” analysis of human psychology extraordinarily complex.
There is then an additional issue: the matters of physiology and environment do not exhaust the human being: there is the entire spiritual, God-ward aspect of human life which is not even considered. However, that spiritual aspect is the most important aspect of human life. Yet, all “scientific” analysis of human psychology purposefully ignores the single greatest element of human psychology: that is like trying to study daytime while excluding all consideration of the sun.
Finally, human psychology has been profoundly affected by sin (our own sin, sins against us, the effects of sin generally). Sin is irrational and thus not capable of scientific methodical analysis: you cannot make reasonable that which is unreasonable by definition.
There are other aspects of this argument (such as pre-commitments)– and it is obviously not a full theory.