Why are parallel fifths against the "rules" in classical composition?

Because they are. No one knows exactly why. Says Wikipedia:: Singing in consecutive fifths may have originated from the accidental singing of a chant a perfect fifth above (or a perfect fourth below) the proper pitch.

Whatever its origin, singing in parallel fifths became commonplace in early organum and conductus styles. Around 1300, Johannes de Grocheo became the first theorist to prohibit the practice. However, parallel fifths were still common in 14th-century music.

The early 15th century composer Lionel Powers likewise forbade the motion of "2 acordis perfite of one kynde, as 2 unisouns, 2 5ths, 2 8ths, 2 12ths, 2 15ths," and it is with the transition to Renaissance-style counterpoint that the use of parallel perfect consonances was consistently avoided in practice. Composers avoided writing consecutive fifths between two independent parts, such as tenor and bass lines. The fifths did not have to be undisguised, or the only two notes of a melodic line.

The interval may form part of a chord of any number of notes, and may be set well apart from the rest of the harmony, or finely interwoven in its midst. But the interval was always to be quit by any movement that did not land on another fifth. The prohibition concerning fifths did not just apply to perfect fifths.

Some theorists objected also to the progression from a perfect fifth to a diminished fifth in parallel motion; for example the progression from C and G to B and F (B and F forming a diminished fifth). The strict avoidance of consecutive fifths is one of the major reasons some musicologists doubt whether Johann Sebastian Bach composed the famous Toccata and Fugue in D minor. Bach was an accomplished composer, highly skilled at avoiding consecutive fifths, but the toccata abounds with them.

However, more recent arguments suggest this is not the case at all, and that the Toccata was written by Bach but written for violin and transcribed for organ. The identification and avoidance of perfect fifths in the instruction of counterpoint and harmony help to distinguish the more formal idiom of classical music from popular and folk musics, in which consecutive fifths commonly appear in the form of double tonics and shifts of level. The prohibition of consecutive fifths in European classical music originates not only in the requirement for contrary motion in counterpoint but in a gradual and eventually self-conscious attempt to distance classical music from folk traditions.As Sir Donald Tovey explains in his discussion of Joseph Haydn's Symphony no.

88, "The trio is one of Haydn's finest pieces of rustic dance music, with hurdy-gurdy drones which shift in disregard of the rule forbidding consecutive fifths. The disregard is justified by the fact that the essential objection to consecutive fifths is that they produce the effect of shifting hurdy-gurdy drones.

Per Wikipedia, "During the common practice period, the use of consecutive fifths (or parallel fifths) was strongly discouraged. This was primarily due to the notion of voice leading, which stresses the individual identity of the parts. Because of the powerful presence of the fifth above the fundamental in the overtone series, the individuality of two parts is weakened when they move in parallel fifths."

Why did the classical and baroque composers avoid the parallel fifths like the plague? My guess is that they may have gotten sick of hearing overplayed parallel fifths, which had been played since the Roman regime. It was considered "cool" during their time (post-Renaissance) to innovate something the ancients didn't know, so they must have decided to make voices more distinguishable.

Why do music majors still study parallel fifths? My guess is that you are being equipped with the best practices of the past, including those not in accordance with your personal tastes and preferences. In the future, you may find a particular use of something you find useless now.

I don't agree with the imposition much, but I don't think it hurts to learn a little of everything.

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