And maybe get rabies doing it. You don't get the point. You don't want your dog to win a fight with a wild animal, you want the fight to never occur.
Coyotes won't approach a human unless starving, protecting babies, or rabid. All three can easily occur with our encroachment on their land and severe winters making food scarce.
Taking the chance of your dog having contact with a wild animal just isn't worth it. Shoot at a safe distance, these buggers can run FAST.