As a solo sport, rock climbing is akin to running or unicycling in terms of personal challenge. While climbing buddies often engage in friendly competition, most climbers are primarily focused on improving their own abilities and pushing beyond their personal best, without worrying about what others might be doing. Climbing is about you, your relationship with your body, and your relationship with the rock, and even when its frustrating or painful, the rewards can be really fantastic when you finally push through something "impossible" for you.
My favorite thing about climbing is the inherent life metaphor available in every moment on the rock. Every route is a microcosm of life: there is a goal up there (visible or not) and to reach it you must move past challenges large and small. As in life, you choose which goals you chase, knowing some are tougher to reach than others. And sometimes the hurdles in our path seem insurmountable, but with time, effort, and much noodling, even the most intimidating barriers eventually fall.
Since climbing helps us be really in-the-moment, you can get really wrapped up in the minutiae of a particular sequence, let it drive you crazy, bang your hang against the wall (metaphorically), and really embrace a challenge. But anytime things get too intense, you can sit back and let it all go. Because it's just rock climbing! It's fun! And there's no better way to put your other life challenges in perspective.