Panting can be a sign of stress in a dog - why do you tell children that panting dogs are happy?A panting dog is dealing with the stress by panting. A stressed dog that is not panting is much more dangerous because it has no mechanism to relieve the stress and is therefore more likely to react. Not all stress is bad stress. The dog might be waiting for a child to come and say hello. The waiting and wondering causes mild stress and the dog starts to pant. "Are we going for a walk?", "Are you going to throw that ball?", "Am I getting the cookie?" These are all circumstances that will cause panting due to mild stress and anticipation. We are trying to keep things simple for children and not providing an exhaustive course in dog behavior. Children obviously cannot be expected to tell the difference between a dog panting under mild stress or a dog panting with rapid frantic breaths that indicates extreme stress (still a dog less likely to bite than a highly stressed dog that is not able to pant).
Other things that the children learn during the program should prevent them from interacting with a dog panting out of extreme stress. They are taught to stand sideways and allow the dog to come to them to sniff their fist. A very nervous dog is apt to move away and not come forward to sniff - so they would leave that dog alone. They may also see the half moon eye, yawn, lick or the fore paw lift and realize that the dog is anxious. They are taught that if the dog stops panting if they come closer, that the dog does not want to meet or interact with them. Hopefully, handlers whose dog are very anxious will say no, when a child asks to pet the dog.
So for the most part a panting dog is a dog waiting with happy anticipation for something good to happen, or at least is a dog that is dealing with its stress. The panting/not panting differentiation is simple for children and immediately rules out many dogs that they may otherwise have wanted to pet and gives them a way to decide whether their own dog (who is the one most likely to bite them anyway) is open to interaction with them. We also teach that children should ask the dog handler to tell the dog to sit before they meet it. The cue "sit" is a stress reliever for most dogs because it is familiar and generally has a positive association and gives the dog some control of the situation. A dog that does not sit for the handler is not under sufficient control for a child to pet. An extremely anxious dog is unlikely to follow instructions and is ruled out on that basis, whether panting or not.
To summarize (so that a child can understand):
Panting and wiggly = safe
Not panting and stiff = dangerous