What makes people irrational thinkers?

[vulcanlogician]

Jung was careful to differentiate what he called the psyche (Psyche in his German) from the soul (seele). I suspect he revived the earlier Greek word (with a new meaning) to specify its difference from the more common German seele.

What he called the psyche included the whole set of processes, conscious as well as unconscious. What he called soul was more like personality, or a function complex. It was less than the whole psyche.

And yet another "soul concept" is present in Jung's model: the anima (Latin for soul)... which, particularly in men, represents our sense of soul, our feminine self, an intermediary symbol that greatly influences our unconscious. It seemed Jung used many soul concepts to help him describe the goings-on of our inner world. But when he describes the whole mental system as "psyche" including inner drives, capacity for reason, the whole shebang... I think his use of the word equates soul with mind. Jung was heavily influenced by Nietzsche.

All that aside, philosophers have tended to equate mind and soul due to Descartes influence. I'm following in that tradition. It might differ somewhat from Plato's conceptions, but not entirely. There are similarities between the Platonic soul and the Cartesian soul.

Plato had no concept of an unconscious mind. For him, mind is thinking consciously. 

As you say, he did think we might have memories from before we were born which could come to the surface, but there was nothing like the active, ongoing, affective unconscious of Freud or Jung. 

There are hints of an unconscious mind as early as Plotinus, and Paracelsus thought we might be perceiving things which we weren't aware that we were perceiving. But the term was coined in the 19th century by Schelling (Unbewusste), and translated as "unconscious mind" by Coleridge. 

So I'm not sure how Plato's ψυχή resembles Jung's, except in name. They are structured and function entirely differently. 

True that Plato didn't elaborate on the unconscious, but nonetheless I've always been intrigued by the similarities between Freud and Plato. Both had three-parted models to describe our inner world. There is no 1:1 reduction between the two, but similar dichotomies are present in both. Both models have a rational ego trying to manage urges that spring from the body. Jung's model differed from Freud's, sure. But one cannot deny Freud's influence on Jung.

The thing about Freud and Jung were, they were both trying to identify the cause of neurosis, and this makes their descriptive models themselves somewhat neurotic. (Freud more than Jung, to be sure.) Jung saw the ego as "in orbit" around the greater psyche. Jung's method involved introspection, peering into the unconscious and identifying which symbols the Self was using to communicate with the ego. Through a process of individuation, one might come to understand impediments to the general psyche, and ego functioning. Because Jung had this goal in mind, his method of observing the psyche was slightly biased to include the symbols that help untangle neuroses. Hence Jung's model is somewhat neurotic itself. I don't think we even need to go into how Freud's model is neurotic. I mean, yeah.

In any case, it's interesting to analyze how much early thinkers like Plato and Plotinus described (or didn't describe) an unconscious mind. At first thought I want to say that Plato broached the subject, but, yeah. You are correct to say he mostly tried to understand the conscious mind.

So, in conclusion I want to say that each thinker had his particular take on the soul/psyche. But ultimately, Jung, Freud, and Plato were (more or less) understanding the same phenomenon. Going forward, I'm going to keep "conflating" soul and mind in a quasi-Cartesian way. It's just how I roll. I may be somewhat in error to do this, but I think I'm not too far off the mark. I'll address errors on a case-by-case basis. But as far as I define it, soul is (more-or-less) the same thing as mind.