I shoot wood arrows because I prefer to make my own gear. What we get out is directly proportional to what we personally invest... and I want to get as much challenge and satisfaction from this as I can.
I usually shoot hickory arrows, sometimes arrows from wild shoots of viburnum, rose, etc. and have for almost 20 years now. I barrel taper the hickories and match them VERY closely in the process. Except for maybe a solid fiberglass bowfishing arrow, I've shot nothing as tough as hickory.
Another reason I shoot wood arrows is following crafting a selfbow from scratch, it wouldn't seem right going to the store to purchas mass produced arrows to shoot from it.
Performance wise, wood arrows leave me wanting absolutely nothing, so other materials don't even draw an inquisitive glance from me. They're just easier.