Freud, because of his deep insecurity, (we have to remember he was the one psychoanalyst who didn’t have a psychoanalyst) desperately wanted psychoanalysis to be scientifically respectable — scientific — a science. He tried to prove that it was, but his proof is flawed. Invalid, in fact.
It’s a great shame. If only he’d had the courage and confidence to say ‘Actually, I don’t give a nun’s wimple if it’s scientific or not.’ Then he wouldn’t have laid psychoanalysis open to those repeated criticisms that it isn’t ‘after all’ scientific.
The psychoanalysts — or perhaps they should be called metapsychoanalysts — who almost as desperately try to prove that it is, ‘after all’, scientific, are barking up the wrong tree: it isn’t scientific, (which is not to say it can’t use, just as literature or painting do, scientific methods and tools), but it doesn’t matter. There are more ways of relating to the world than the scientific one.
Don’t worry, (yes all right; nobody was), I’m not about to trot out the hoary idea that psychoanalysis is an art — though it’s worth pursuing that some way — I’m rather more concerned to say why it isn’t, indeed can’t be, scientific.
It’s because the most important concept of psychoanalysis is the Unconscious. And the Unconscious is, in one respect if no other, like God: it is unknowable. If we know something, we are conscious of it. And so whatever it is, it’s not unconscious. Nothing can count as evidence for its (his) existence, so, by the positivist criteria of science, it makes no sense to talk of ‘God’ or ‘The Unconscious’. There are those who simply know that God exists: that is to say, they are privileged to have been made aware in some way of the spiritual dimension. And if you haven’t been made aware of it, you haven’t, indeed you’re likely to deny its existence.
Similarly, there are those — quite a lot of thoses, among them those who have been the subjects (it’s the wrong word, but there hasn’t yet been found a right one) of psychoanalysis, who simply know that the Unconscious exists.
So there. Science Schmience.
 On re-reading this, I see I’ve committed a logical sleight of hand here: I have confused the object of thought with the thought of the object. The point, however, is that, for simple logical reasons, one can no more ‘know’ the Unconscious than one can look at something that is destroyed, or at least changed into something else, by light.