I'd say that riding isn't cruel. As was pointed out, some people make owning a horse cruel. One needn't keep their horse in a box stall or leave shoes on them (there are alternatives), and if an animal isn't afraid, it's not cruel to put them into horse trailers and haul them about.
Sometimes what appears cruel is only the perception of the person watching. You may be forced to do something that could, to someone who doesn't know any better, look mean and heartless. Wild horses are gathered off the range and squeezed into chutes where they're tipped onto their sides for vaccinations and hoof trimming before sending them into a corral full of other untamed animals, never to return to their freedom. They're full of fear and distrust. Is it cruel? The alternative is letting them die of starvation or thirst out on the range. Which is worse?
I think most bucking stock is cared for better than the general horse population, too. For an eight second ride he may be madder than a hornet, but he's not going to be hurt any worse than most of our horses are if they feel the spur at some point in their lives. You don't see the horses leaving the arena with blood dripping from their sides; the rider is an annoyance more than anything, and the rope doesn't hurt, it's just irritating.
The one 'sport' that I can't handle is bull fighting. I don't care how well it demonstrates horsemanship (and those guys can ride), it's a danged cruel thing to do to both the bull and the risk to the horse is too great.