I'm disappointed by the comments which suggest this is an unimpotant topic. The way music is taught is crucial - whether to adults (as in the OP), or to children.
I suffered horribly as a small boy at the hands of boarding school staff who shared the OP's views, being punished more for my 'crime' of refusing to learn to read music precisely because I had 'precocious talent' (I still have the reports).
People do need to understand the different elements and core skills that feed into musicianship, and the relationships between them.
Music is about emotion and beauty. How you get there varies from person to perdon, and teachers should understand what matters for individual pupils