One of those penny-drop moments came to me when, as an undergraduate playing through some music I had written as a younger teenager (and finding it both better and worse than I remembered - does this happen to everyone when revisiting the efforts of their younger selves?), I came across a bit I'd always had to play quite carefully to make it sound okay. It could work all right, but if you didn't place it just so, it could sound a bit naff.
In the time between writing this music and revisiting it, I had been taught the concept of consecutive 5ths and 8ths, and the importance of avoiding them. This concept now revealed to me what the problem had been with my piece of juvenilia, and simultaneously made me grasp, emotionally, why I should care about this bit of theory.
There are other schools of thought on consecutives of course. Take Noel Coward: