As with any skill, learning music requires that the student learn some important musical concepts. These concepts are purely music related (not directly related to other skills, although similar to mathematics), and are in addition to the physical skills required to play the instrument. These musical concepts coupled with reading music fall under the heading of "Music Theory". The design of the piano is particularly conducive to learning Music Theory because the keyboard is logically designed and visually accessible. The same musical concepts when applied to other instruments can be quite difficult to understand and master.
Reading Music: All musicians SHOULD learn to read music for the same reason everyone should learn to read their mother tongue (English). It allows the musician freedom to explore and learn new music for the rest of her/his life. Musical notation is a system unlike any other, and requires just as much time to learn as reading a language does. First the student must learn the alphabet (in this case, the musical symbols and the association of lines and spaces to specific musical notes). Then, the student must learn to read groups of notes as a single musical concepts (chords, scales, etc.). Finally, the student is able to read music as one reads a book: entire concepts (musical gestures) are recognized immediately, and translated into the actions of playing the instrument. Just as a student must study reading for 12 years to be able to read most everything that is in print (with the occasional aid of a dictionary), a musician must study music for just as long to be able to learn any new piece of music he or she chooses.
Understanding How Notes Work: The music student must not only be able to read the notes on the page, but must fundamentally understand how they work. Just as the letter "e" is pronounced differently in each of the following words: "feel", "weigh", "time", and "souffle", the musician must understand how the notes work when grouped as chords, scales, intervals, etc. Years of study and practice are required to understand Music Theory, and its application to each instrument is quite different, just as the letter "e" is pronounced differently in the Spanish word "señor", the French word "beux", the Italian word "fine" and the German word "bitte".
Piano Makes Theory MUCH Easier: On the piano, the keyboard is structured in a pattern that closely resembles how the sounds work in musical theory. Each key produces a specific pitch. The white keys represent the note letter names: A, B, C, D, E, F, G and the black keys represent the sharps and flats: F# and Bb, etc. When describing the structure of intervals and chords, the student can see the keys directly and recgonize the patterns. Piano students are capable of understanding and playing music of a much greater complexity (from a musical theory standpoint) very early on, when compared to students of other instrument.
Theory Difficulties on String Instruments: The student must learn where to place the fingers on the string without any visual guides, in order to produce the correct notes. This includes where the fingers are placed to start, how far apart the fingers are, and where to place them when the hand moves. Without a solid foundation in music theory using a keyboard with visually understandable keys, the string student will find many theoretical concepts very difficult if not impossible to understand, and may take many additional years to master.
Theory Difficulties on Wind Instruments: Although some finger patterns follow some logical sequence, for the most part the fingering of wind instruments is a very large set of separate and unrelated patterns. These finger patterns do not relate well to the music theory, and do not help the student to understand the theory. Wind students often have the most difficulty understanding concepts of chords and harmony, despite the importance of this knowledge to their playing ability.