A suspension trainer is safer than many other types of exercise for several reasons. The first reason is that you are allowed to move freely. With gym weightlifting equipment, you are forced to move in a very particular direction over and over. If something isn't correct, this can cause injury. With suspension training, you move more fluidly and in the natural directions your body needs to go.
The second reason is that you can automatically adjust the intensity just by adjusting your body position or how deep you go into the movement. If you are using weight lifting equipment, either free weights or a machine, the exercise or weight might be too much and you need to stop and adjust. This can throw you off but also cause injury in extreme cases. Even in the middle of a movement, you are able to adjust with your suspension trainer.