Dreams allow us access to our collective unconscious- a collection of ancestral memories that are common to all of us.
Our collective unconscious is our ancestral memories. We share it with all other members of our species (and perhaps some other species closely related to us).
When we dream, we connect our personal memories to our ancestral memories. There are elements of our dreams that are personal to us (for example the memories of the previous day) but there are also universal symbols received from our collective unconscious. In this respect, dreams can be interpreted to provide information on the individual and the collective. For example, putting a sword in a sheath might be a universal symbol for sexuality, as gleaned from our collective unconscious, but the individual's unconscious decision to dream about a sword, as opposed to breaking down a door- another symbol for sexuality- is revealing of the individual's psychological state. In this respect, dreams can have a multitude of meanings, and the accurate interpretation is not always immediately obvious. However, the existence of a collective unconscious and universal symbols means accurate interpretation is always theoretically possible. There is also evidence for this in our innate behaviours and universal responses to stimuli. For example, humans have a predisposition to fear snakes. This is likely because, in the days before anti-venoms, snakes were a genuine threat to our lives. Snakes are also a common theme in dreams, regardless of whether or not the individual has a snake phobia, suggesting that a collective unconscious can, and does, influence our dreaming.
The idea of a collective consciousness that is passed down through a priori and innate knowledge from generation to generation is essentially a form of Lamarckian evolution. Lamarck famously suggested that a giraffe got its long neck because one giraffe was able to stretch its neck during its lifetime and then pass this trait onto its offspring. If our ancestors were able to construct new personal memories in their lifetime, then impart these memories into their offspring through a collective consciousness (ancestral memories), then this would essentially be a variation of Lamarckian evolution. As a variation of Lamarckian evolution, dream interpretations relying on the notion of a collective unconscious are vulnerable to the same criticisms as Lamarckian evolution. Of these there are many. For example, if a man loses his arm in an accident, his children are not born without an arm. Changes acquired during a lifetime, be it physical or psychological, are not passed on to offspring. Only those present in genes can be passed on. Nobody would suggest that our memories can affect our genetic structure and allow us to pass on a collective unconsciousness to our offspring in that way.
[P1] Our dreams are an amalgamation of our personal unconscious and our collective unconscious. [P2] Our collective unconscious is shared. [P3] Therefore, symbols in our dreams derived from our collective unconscious have shared meaning and are knowable. [P4] Therefore, dream interpretation is theoretically possible.
[Rejecting P2] A collective unconscious cannot be shared as it cannot be passed on from generation to generation. [Rejecting P4] Therefore, dream interpretation is not possible.