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It should be mentioned that a muzzle is not a solution for dog aggression, be it towards other animals or towards people. The muzzle is a tool to be used in a training program to solve leash reactivity. Leerburg sells a very good online course on Leash Reactivity.
There are a number of medical issues that warrant a dog wearing a muzzle. Simply visiting a vet with a reactive dog is probably the most obvious, but stopping a dog from licking bandages can be just as important. If a dog has had surgery a muzzle may be used to eliminate the dog wearing a neck cone. This is something to discuss with your vet.
Wearing a muzzle may eliminate a reactive dog bite with an injured dog. Police K9 handlers often carry a cloth muzzle for that very reason when they deploy with their dog.
Some dogs have a habit of eating things they find on the ground (rocks,garbarge,animal poop, sticks and other foreign objects) Muzzles eliminate this problem
Some dog sports require a dog to perform specific obedience exercises in muzzle, French Ring Sport and PSA are two sports where a dog must wear a muzzle in competition.