Although there is already a selected answer, I wanted to provide some additional historical information. I've recently been reading about 18th century music pedagogy (particularly Sanguinetti's The Art of Partimento, and Gjerdingen's Music in the Galant Style) and your question fits in really well with what I've been reading.
In particular, music theory in the 18th century was taught in a very practical, empirical style, via the practice of improvisational accompaniment to a thoroughbass. As you became proficient with accompanying, you would naturally pick up on various voice leading patterns that you would see repeated over and over again, much like how a child learns language through repetitive use and immersion. Eventually, you would move on to accompanying a partimento which was a step beyond simple figured bass accompaniment, in that it also entailed improvising melodies and using imitation, in order to make a proper piece of music (such as a sonata movement, or even a fugue).
This tradition was especially prominent in Naples, which at the time, was one of the primary centers for musical learning in the world. Here there were multiple "orphanages" sponsored by aristocrats that took in children and taught them various useful trades, one of which was music composition. Indeed, Gjerdingen stresses the point that 18th century music wasn't so much a matter of personal expression, as it was a craft to create a product for a patron. "The notion that a sad piece by the court composer was about the composer's sadness would have seemed just as strange as the idea that a tart sauce prepared by the court chef was about the chef's tartness."
Sanguinetti also describes the later responses of 19th century musicians who looked back upon this practice and asked a question much similar to yours:
whether the better system to introduce to a student the art of
composition is that used formerly in Naples, i.e. to study the harmony
practically through the accompaniment of a through bass (partimento);
or rather, as often happens nowadays in imitation of the Germans, to
study the harmony starting from theory.
At least one response, from the Resident Academician Ettore De-Champs "answered that a study of harmony, as well as of languages, that begins from the theoretical side is detrimental and cannot result in authentic command of the subject." (Snaguinetti's summary of De-Champs'). Another response from one Riccardo Gandolfi claims that theory had been taught alongside the practice, but that it had only been taught orally. Gandolfi also points out that partimenti were old fashioned, and did not adequately address 19th century harmonies:
[Partimenti] do not include what is required for the study of modern
harmony. There one cannot find a great number of chords that are
common now, such as those altered, in root position or in inversion;
there never appear dissonances in the bass other than the third
inversion of the seventh chord, and the ninth chords are never
employed in all their inversions; as for modulations, only those to
relative keys are employed.... Now I think that in the teaching of
harmony practice cannot be severed from theory, the first being an
application of the second.
Finally, Sanguinetti quotes part of an 1877 essay by one Michele Ruta, who seems to have thought the early masters were keeping something secret by not teaching theory:
Even if the study of harmony was taught through that of the partimento
-- therefore without principles, and in a totally empirical way -- I
nonetheless believe that the great masters who taught it did not
ignore the true sources of harmony and the true principles from which
their ingenuous, little rules sprang... I cannot understand, however,
why they, who could well have regulated the teaching of harmonic
science otherwise, chose to reduce it to a lengthy series of exercises
with neither logic nor principles... Sometimes I suspect too that
those masters of harmony would attribute such an importance to the
figured bass, without explaining the principles, in order to be, for
as long as possible, the only oracles able to interpret those
So the short (and overly simplified) answer to your question as to "why music is taught this way," seems to be a combination of:
- The decline of the aristocracy who could afford to sponsor the
institutions that provided years of dedicated instruction that such
a method required,
- The resulting need to be able to target teaching towards amateurs in a shorter time,
- The increased complexity of the music theory, which used more types of chords and modulations in increasingly freer ways,
- The rationalist, scientific, and progressive German mindset of the 19th century that favored theory over practice, and
- The entrenchment of said mindset becoming the pedagogical tradition in the years since.
Fortunately, we are now beginning to rediscover these older methods, and dust them off. Your description of children learning to create their own musical sentences reminded me very much of this video of the (then-child) prodigy Alma Deutcher performing a back-and-forth improvisation with her teacher Tobias Cramm. My understanding is that Alma's father is a linguist who had read Gjerdingen's book, so when his daughter showed a desire and aptitude to learn music, he looked for a teacher who could specifically teach her using a partimento-based approach -- which was difficult to find. More recently (and she's still only a teenager) she's become a composer who has written several operas, her own violin concerto and piano concerto, and several other works.