The spider entered the dream books carrying its waking folklore with it. European tradition holds the small money spider lucky and a spider at evening a good omen, and the older dictionaries read dream spiders both ways, industry and fortune on one side, entanglement on the other, the web deciding which. The weaver of fate is an old figure besides, and interpreters who reach for the Moirai spinning and cutting thread, or for Arachne weaving against Athena, are drawing on Greek story rather than on any dream manual.
Psychoanalysis took the image up in earnest. Karl Abraham, one of Freud's earliest colleagues, published a paper in 1922 on the spider as a dream symbol, reading it within his school's theory as a figure of the dangerous mother, and the spider has kept a place in psychoanalytic case literature since. The Jungian tradition reads the web rather than the spinner: a patterned structure radiating from a centre, spun from the spinner's own substance, which invites the gentler reading of creative fate.
None of these readings is evidence about spiders or about dreamers in general. They are the accumulated positions of distinct traditions, folk, Freudian and Jungian, and a given dream may answer to any of them or to none.