I don't know much about alligators, but in general, running from predatory animals can signal that you are prey. Alligators and crocodiles can sometimes move surprisingly quickly over a short distance, and although the horse would probably quickly outrun them, a human might not.
Presumably the handler knows that this alligator isn't a threat in this moment, but running away might turn it into one. Also, allowing the horse to run back lose might be a greater hazard than the alligator.
FWIW, I agree with the horse and would want to get out of there, but I reckon the guy knows what he's doing.