Physical Danger
In February of 2010, animal trainer Dawn Brancheau was killed by a killer whale at Sea World in Orlando, Florida. It was the first such incident that the park had ever experienced, but it certainly wasn't the first incident ever involving an animal and its trainer.
When you work with animals—wild or domesticated—there are certain intrinsic dangers. Animals are very good at sending signals to you about what's going on with them, but we're not so good at reading them (at least initially; it stands to reason that an experienced trainer gets to know her animal(s) better than almost anyone else).
But animals can be unpredictable and you, as the trainer, have to know and respect that. A bicycle-riding bear may pose more inherent irritation with you than a maze-meandering goldfish, but have you ever been glared at through glass by an irate goldfish? It's uncomfortable, to say the least.