CrossFit is more than sprints, pull-ups, and snatches, which is to say there's more to it than purely the physical aspect. It's even more than the community-driven social aspect of suffering with your peers and cheering them on alongside you. There is a huge psychological component to this discipline that cannot be overstated.
The community reinforces this psychology, and they take their example from the gym's ethos (generally established by the coach). I will attempt to break down the ethos that I personally strive to maintain in the gym here.