Why did the old rules of counterpoint forbid parallel fifths?

Parallel fifths were forbidden because they make two voices that are meant to be independent move as one. Counterpoint is the relationship of two or more simultaneous musical lines that are harmonically dependent on each other, yet independent in rhythm and melodic contour. When two voices run in parallel perfect fifths, the perfect fifth is among the most stable of intervals, so linking the voices that closely interferes with their independence much more than parallel thirds or sixths would.

The rule has a history. Singing in parallel fifths was commonplace in early organum, and around 1300 Johannes de Garlandia became the first theorist to prohibit the practice. The convention dates approximately from 1450. In 1725 Johann Joseph Fux turned it into a classroom method in Gradus ad Parnassum, where parallel motion of perfect consonances is strictly forbidden in species counterpoint. Haydn largely taught himself counterpoint by reading Fux and recommended the book to the young Beethoven, and Mozart had a copy that he annotated.

Why the ban, exactly, is a live question. One answer is independence. Another says the fifth is the primary harmonic interval, the one that defines the key, so two in a row raise doubt about the key. A third is social: the ban distanced classical music from folk traditions, where parallel fifths are common, and Donald Tovey said the objection is that they sound like shifting hurdy-gurdy drones. Since the nineteenth century the rule has loosened, and guitar power chords are built on the very thing the old rule forbade.