The teacher is going to teach how to play music on a piano. So he has to:
- understand how the piano works
- understand how to use the body for playing the piano
- understand how music works, and how piano music works
- understand music theory in a practical way both for written music and in the music we hear as we play, as well as how this meshes with the instrument: from note recognition, chords, progressions, and more
- know how to TEACH these things so that they come together
- and so, know how a student develops in music, how various types of students might develop
- how to get a student to get at skills during lessons, to "get" things
- how to guide a student's practicing between lessons
- do so without intimidating a student on one hand, or neglecting the student's development on the other.
In summary: skills in playing, understanding music, and teaching.