Composition is actually taught (and learned) only partly objectively, with the rest being taught subjectively. Broadly, there are "mechanical" aspects to composition that range from critical to helpful in importance. At the same time, every composer has to find their own process and "voice", so there are ways to help composers do that, but it is essentially a subjective process.
The objective aspects of composition are probably already clear. Music theory, the ranges, timbres, and loudnesses of different instruments, and even what we might call "tropes" or forms and how they typically are interpreted by listeners comprise the bulk of the important objective knowledge needed for effective composition. Many have composed without solid knowledge of all of these areas, but knowing as much as possible does help a lot. Every composer has to have some way to "fix" their compositions, whether writing sheet music or recording ideas or just jotting down chords, so teaching how to read and write music and/or record and produce music are also important objective aspects of composition.
For the subjective parts, obviously there's no body of knowledge that can be transferred, but it is possible to lead to students on processes of discovery. One time-honored way to do that is to give compositional assignments that start small and grow in complexity and originality.
An excellent example of a leading exercise for composition is an assignment to write a two-part invention. One way to make it easier for beginning composition students (who should already be adept at writing short four-part harmonies either given a predetermined chord progression or soprano or bass lines) is to have the students come up with their own motif or subject and then create a countersubject. From there, students can be told or allowed to model their inventions on existing inventions, perhaps by Bach.
That process begins with analyzing the invention that the assignment will be based on, writing the Roman numeral analysis on the score through the whole invention, as well as marking the major sections, key changes, and often circle of fifths progressions and cadences. Students might also be asked to note any suspensions or other types of dissonance.
From there, the original invention can/must be followed. Perhaps the student picks a beginning key and then creates the same harmonic structure based on their own melodic motif. The easiest way to complete such an assignment would result in an invention that has exactly the same number of measures as the original, with exactly the same harmonic movement from chord to chord and measure to measure.
Writing and adhering to the form and traditions of a baroque invention turns composition into a problem solving exercise. You generally have to alter the motif in interesting ways to follow the harmonic structure of the original invention without unstylistic dissonance. And it is much easier to write a development section when you have the subject and harmonic structure already decided. Such an assignment teaches students how composition can often be a process of creating and then solving problems for oneself. Having completed such assignments, it was a surprise to me how much I grew to be frustrated with my original motif as I tried to work through the development section, while at the same time learning that every motif/subject will present different challenges when one is trying to develop it within a predetermined structure.
Subsequent assignments can range from single movements in sonata-allegro form to entire symphonies. Each assignment can (and arguably should) have different rules and restrictions, which help prevent students from feeling overwhelmed. The fewer choices you are allowed to make in the beginning, the less pressure there is to "be creative".
If you're skeptical whether such exercises help develop each student's individual creativity, I have some responses (which you may or may not accept):
- This is a time-honored compositional education strategy that has been used by many to learn composition.
- The incremental nature of the exercises gradually builds the creative requirements and asks more and more original content from the students.
- Artistic creation is, in more ways than you might expect, largely about problem solving, not about inventing something from nothing. Generally, a very small amount of raw inspiration is the germ from which a large work of art that is broad in scope is grown in a mostly mechanical, problem solving process. The initial idea(s) lead the artist to the subsequent ones, and at some point the restrictions and structure form the snowy slope that the tiny snowball idea is rolling down, gaining mass and momentum, until the huge snowball/avalanche is formed seemingly on its own. 1% inspiration and 99% perspiration applies just as much to the arts as it does to invention.
- Not only is it hard or impossible to teach creativity, you don't have to. Humans are inherently creative. Once you've given a person the tools to create, they will start creating. Now, that doesn't address the subjects of taste or artistic honesty and integrity. I personally believe that a creative professional with the tools and training will be inspired to create work that only they can create, and while it may be small, there is some kind of audience for almost anything that is the result of diligent and thoughtful hard work.