At one point, overcome with emotion at the beauty of the mountain, Whymper says that it would be "vain to attempt to describe it," because words would not do the view justice. I think this does help answer one part of the question "why climb?" and it actually paints climbers in a somewhat more favorable light than we sometimes do ("they're stupid, it's not worth it, etc). The reason for this is that these is obviously an incredible aesthetic value in the outdoors that seems to resonate with certain people more than others--we don't begrudge artists their pursuits despite the fact that they are inherently centered on themselves, yet we seem to--in class--begrudge these climbers their pursuits because they are selfish. I think the aesthetic value would usually allow us to empathize with their motivations more, simply because while putting your life in danger for an unquantifiable accomplishment seems like something we can universally understand (and condemn--althought I'm not sure it's true that we do universally understand), taking individual pleasure in the scenery is judged by altogether different guidelines. We don't assume that this experience can be universalized, and are thus much more hesitant to condemn this as a reason for climbing.
The next question, however, is why write about these experiences? If the aesthetic is the reason for the climb, but it cannot be put into words, then the writing of the climb seems to fall back into either the self-glorification or the obligation-to-tell-for-purposes-of-expanding-knowledge category. Both of these categories are ones we've grappled with all semester, so while Whymper's text might give us more insight into climbers' motivations, it still leaves us without answers to the "why write" question.