I'm probably the one person on any dog forum who will say this, but... when my dogs are frightened or upset, I do comfort them. I don't coddle them in a way that indicates that I'm fearful too, or in a way that reinforces fearful behavior, but instead I try to be confident and soothing at the same time. Sometimes I'll ask for kisses, which they do gladly, with tail wags, and distracts them from whatever they're fearful of.
I can honestly say I can't think of anything they're fearful of any more, even when one of them got hurt the other day... so it seems that the "don't comfort them when they're scared" theory doesn't hold water. I suspect that that theory was developed by someone who believes dogs don't experience emotions like fear or love, that they only exhibit behaviors that we project to be those emotions. IMO, that is bunk. I used to believe that too, just because that is what I was always taught, but after having dogs for most of my adult life, I have zero doubt that my pups experience emotions, and if they need some comforting, I'm going to give it to them! I love having the confident, happy pups that results from this approach.
