Okay, so what could be dangerous about picking out the right card or pulling a rabbit out of a hat?
Typically, magic is a very safe career. There are no real supernatural powers involved. You and your manual dexterity are in total control. It's when you start incorporating dangerous stuff into your routines that the chances of harm increase.
Some magicians swallow swords, or perform with fire, or sit in boxes over the Tower Bridge in London (because, magic?). Believe it or not, no doctor would ever recommend anyone do these things.
Remember Roy of the Tiger Twins from earlier who got mauled by one of his co-workers? It can totally happen. And that still was only considered an "accident" rather than "the tiger wanted to eat him," because a magician doesn't blame their tricks going wrong on anyone or anything else—not even a hungry tiger.
Even Houdini had his close run-ins with death. Really though, you can't honestly tell us that locking yourself upside-down in a tank of water while wearing a straitjacket is a reliable way to make money.
Then there's the infamous "Magic Bullet Catch." Maybe it sounds like the trick involves catching a bullet? It certainly does—with your teeth. The whole point of this trick is to not die. Unfortunately, that hasn't always been the case (source).
Most of the time magicians won't face death, and those who do face bodily injury will be performing a trick they've rehearsed to perfection. The biggest takeaway here is to know that while your magic may be fake, the danger can be very, very real.
Also, don't try to catch a bullet with your teeth—we're just saying.