Physical Danger
Since your entire career is based around using and maintaining your body, there's always the underlying danger of injury. Muscle strains and tears are the biggest issue, so it's important to make sure you stay loose and never try to show off, even if showing off is kind of why you became a fitness instructor in the first place. Unless you're strictly yoga, you'll likely use weights and even exercise machines in your training, which come with their own level of physical harm-abilities.
Besides outward strains, there are also internal issues that can arise when teaching groups of strangers/gym friends how to stay in shape. People with heart conditions or asthma might want to reconsider this career choice. Your heart rate will often be elevated, so you'll want to manage any anxiety disorders that may be present.
Add to this the natural human condition of the body breaking down, which the scientific community calls "getting old," and you can see how staying safe is a daily concern for the fitness professional.
On the bright side, since you're so well trained, you'll also know both how to avoid injuries as much as possible, and what to do when they happen. Also, being the in-shape person that you are, your body will likely be better able to handle the kinds of strains you'll be putting on it. That doesn't mean go out and do five hundred squats just because you've got great glutes, but should you ever need to bend and flex, your body should be able to handle it.