If I had to choose a single element of music theory that has most interfered with my understanding of how the ear works it would be the notion of tonicity.
More important to the ear than the tonality of a composition is the history of what and how one hears, in other words, the tones in the order in which they are presented. Just because the tonic may come first does not mean it is a solid tone--I can think of several examples of works that begin with unsettling tonic tones or even triads.
Taking the first tone of every composition seriously also illuminates the beginnings of many interior movements and many single pieces within a cycle: often the first tone can only be understood in relation to the last tone of the preceding movement.