When I first had the idea to delve into the [unnatural] beauty of soccer in a previous post, I had planned to juxtapose the two biggest passions I've had in my life, rock climbing and soccer. I hoped to highlight their uniquely natural and unnatural qualities, respectively. In the end I found it more appropriate to address them separately. Now I am not naive enough to claim that climbing is the most physically natural activity for a human to take part in. That title of course belongs to the long-distance runner, as was so eloquently articulated in Christopher McDougal's Born to Run. I would argue however, that as a holistic activity, you won't find anything more natural than climbing.
First off, climbing incorporates tools like quickdraws, shoes, and rope. Given our limited physicality, our species wouldn't make it all that far without tools. This quality in itself of course holds very little weight, since nearly any other activity can claim the same.
Secondly, climbing incorporates a unique mix of desire for achievement and communal support. We as people are inherently selfish (or at least that's what Plato taught me). This isn't necessarily a bad thing, but our motive for action, whether driven by greed or a desire to "feel good" about ourselves, is inherently selfish. Climbing allows us to pursue each of the most basic desires related to accomplishment. There is of course the opportunity to challenge ones self and pursue personal goals. There is also often a sense of communal achievement, most notably in the case of multi-pitch climbing and mountaineering. And finally, there is the opportunity to help others (the most unselfish self-serving desire). Particularly when bouldering, there is a reason the routes are referred to as "problems"; they need to be solved, and helping someone else solve their problem can be equally as satisfying as sending it yourself.
Lastly, I'll address the physical. Is there any other sport that is so obviously an attempt to recapture physical attributes of our ancestors? Climbers for years have quite literally studied the movement and techniques of apes in order to perfect their trade. Climbing efficiently may not be where evolution has taken us, but it is truly incredible how successful some have been in imitating our evolutionary cousins. It would be difficult to find a more striking ape impression (apart from Andy Serkis) than Dan Osman, seen below.
Whether you agree or disagree with my claim, I don't think it makes climbing any more or less special. It's in our nature as climbers though, to continually ask the question "WHY in the hell do we do this?!". I suppose this was my feeble attempt at an answer.