For me, "traditional archery" is the pure enjoyment of archery. It's romance and intrigue all wrapped up in a perfect target shot at an unknown distance. Or the imaginings, soft as a whisper on the wind, of the spirit of a Bear; breathing in your ear, "A little closer son, just let him take a few more steps..."
Your shadow on the ground, with recurve or longbow limbs bent in a beautiful arc. The sight of a perfect ball of feathers, spinning into the center of your 'spot'.
I can take some joy in a well executed shot from a rifle, or even a compound...for about 5 minutes. I can shoot my "stick" bows for all day, and go to bed wishing for more light.
I believe there are a few "epiphanys" left out there, especially for those of us who grew up in what was, by and large, quickly becoming a compound era. --The first time it all comes together, whether at the target mat, or in the deer woods... That first good pull on a bow you built yourself... Each will have his or her own (that probably differ greatly from mine). To others, it's just what has always been right.
For some it's a hobby, to some a sport, still others consider it a way of life; a means to an end, or a new beginning. Food for the soul, or just a perfect past-time, it's some good stuff!