Rock climbing is dangerous, but so is driving a car or crossing the street. In fact, statistically you are more likely to be injured by driving, riding a bike, or walking then climbing. You need to remember that climbing, like any sport and outdoor activity, is only as safe as the person participating in it.
Everything we do in climbing as well as all of the climbing equipment that we use is designed to lessen the risks of climbing and gravity. A rope and protection gear like cams and carabiners are used to keep you from falling to the ground. Your climbing shoes stick to the rock and your harness attaches you to the rope.
Some types of climbing, like lead climbing and bouldering, often have more risk of injury than toprope climbing. As a climber, you will learn to reduce the risks of climbing and chance of injury by climbing smart and practicing safety techniques.