In contrast to objective science, which relies on intersubjectively verifiable observation, the Jungian tradition is based on a different methodological fundamental. It starts with subjective experience, which we know from our own personal introspection and from the reports and narration which others give us. Whereas scientific observation is stated in the third person, subjective experience as a starting point always has to have meaning in the first person, too (although there must be a third-person aspect to it as well, or else it wouldn’t even be relatable).
That this is a methodological fundamental is unsurprising, given the roots of the tradition in psychotherapy: the source of such introspection or narration is either self-analysis or the classic analytic encounter. Certainly this was what Jung had in mind when he insisted, as he frequently did, that his theories were based in experience. (He was wrong, however, in claiming that this made them scientific, in the sense that we normally use when we classify theories so. For that would require application of the scientific method, and one of the main points of the scientific method is to exclude these very forms of subjectivity — precisely because they make observations not repeatable and intersubjectively verifiable.)
But apart from its practical (therapeutic) origins and merits, the methodological fundamental has another important benefit: it enables the theories which build on it to take singular experience seriously — something which is excluded per definitionem by the scientific method. Singular subjectivity (such as in mystic experience or artistic inspiration) is generally not repeatable, and typically doesn’t fall under existing, well-understood conceptual accounts. It needs narrative exploration, metaphorical description, analogical presentation and similar techniques in order to be understood by those who didn’t originally have the experience itself. (It has also been too valuable, historically, in human societies to simply be dismissed because it doesn’t fit into the prevalent world view or cannot be quantified given already-known procedures.)
The fundamental methodological choice is what then leads to the central idea; for subjective experience can be either in the acting or in the suffering mode (the subject can initiate and direct their own thought or behavior, or these things “happen” to the subject, as driven by something else), and the discovery that a subject’s psychology is neither fully under their own control nor simply always controlled by an external object leaves room for the notion of interior, psychological factors which are nonetheless not part and not under the influence and will of the conscious personality.
And note that this is not simply another observation. What is subject to the choices and influence of the conscious personality is, in itself, not something to be observed in the third person, but requires a first-person perspective. (In other words, and to put it in more philosophical terminology, it is not simply a case of self-ascription, but a question of avowal.) Therefore, what falls under the notion of a psychologically effective, yet not conscious factor, is in part discovered by introspection and narration, by analysis and self-analysis. (What discovered thus is what is left when conscious psychology is factored out; hence: the unconscious.) The formation of a notion of unconscious factors which act on a subject and have independent effectiveness on that subject’s psychology then becomes, given these fundamental methodological moves, a straightforward and plausible idea.
From this, finally, derives a basic ontological layout. The notion of a conscious subject which has a first-person point of view is prior in the order of explanation to the notion of external objects (including other persons) and potential other, interior factors (those of the unconscious). But all three must be included on the primary ontological level: all are irreducible. (To try and reduce the external objects to either or both of the others would result in idealism; to reduce both persons and unconscious factors to the external objects would leave us with a bald materialism; and it would be against too much evidence to the contrary were we to eliminate either consciousness or the unconscious by assimilating them to each other. Each of these variants can be consistently formulated, I think, but they all seem extreme and none appears cogent.) So the priority in the order of explanation results, not from any reducibility, but rather from the methodological fundamental. (Which is, of course, itself a theoretical choice and cannot be derived from either the central idea or any of the ontological categories.)