For me, it was to pursue archery in what I consider its "pure" form. No gadgets. Simple. Make it, tune it, and go. Never needing to worry about losing a part, adjusting anything, etc. And if made right and cared for they can last a lifetime since there are no wearable parts.
I also like the smooth draw without sights and I believe shooting a "barebow" offers the most versatility of the bow...and I feel a good traditional bow is the best type of bow to shoot if one shoots in a barebow fashion.
That said, I am curious as to what attracts others to the sport...as I know we are all different.