Mountain Climbing
Mountain climbing, whether you're doing it the traditional way or as a "free" climber, is inherently dangerous. But, the danger isn't in the activity itself, the danger lays in the human error or mechanical malfunctioning that one could experience while ascending a rock face. There's only air between you and the ground, and if your carabiner fails, it's game over.
Assuming the Risks
When you fall to some earlier placed gear, there could be ten or more feet of dead space beneath you. If you fall from such a height and swing (or "whip" as climbers call it) into the rock, you might get pretty injured. But, if your equipment fails or your belayer drops you altogether, it's probably the end for you. Over 24 climbers died in the year 2000 alone, and while technology has improved and rock climbers have become more knowledgeable and preventative, it's still pretty dangerous to be up that high.