I am not sure, except for the fact that it suits me. Perhaps it is because fly fishing (for me, at least) is more of a meditative, introspective activity, compared to conventional fishing.
Or maybe it's the Lone Wolf in me, since fly-fishing is mostly a private experience, even if you go with someone else. I get in a contemplative state to where nothing seems to exist for the moment except myself and the immedeate surroundings, which I fully experience. I become aware of so many things that go unnoticed at other times, such as the feel of cool drafts off the water on my face.... the crisp smell of the water and fragrance of the forest..... the sounds of running water, birds, frogs, and other fauna, breezes through the trees, sometimes creating a symphonic epiphany of the true meaning of life, yet other times as soft as a lovers whisper, with a promise of things yet to come.
Perhaps it is because the discipline and concentration required may have a soul-cleansing effect at times, or maybe it provides a level of mental/intellectual stimulation that I must have from time-to-time, the same reason that chess is about the only game that I play.
There could possibly be some Fruedian, or Jungian conotations to it, or maybe some Kierkegaardian Existentialistic dimensions with overtones of Nieztche that cause me to gravitate towards fly fishing.
It could be a myriad of reasons that I am not consciously aware of, but I do know that it is a large part of my life, for whatever reason.
Semper Fi!