Using interactions with dogs to practice being calm and still on the inside, especially while under stress, is the basic premise of Dog and Dojo. Learning to be still inside is also a basic premise for some schools of Daoism (or Taoism).
Consider this passage from The Taoist I Ching, translated by Thomas Cleary (Shambhala Classics, 1986):
Situations of ordinary commotion are even considered by some Taoists to be better for practice of inner tranquility than are situations of external quiet. In his Annals of the Hall of Blissful Development, the Yuan Dynasty adept Huang Yuan-ch’i says:
People are happy when there is quiet and vexed when there is commotion. Don’t they realize that since their energy has already been stirred by the clamor of people’s voices and the involvements and disturbances of people and affairs, rather than use this power to be annoyed at the commotion, it is better to use this power to cultivate stability. An ancient said, “When people are in the midst of disturbance, this is a good time to apply effort to keep independent.” Stay comprehensively alert in the immediate present, and suddenly an awakening will open up an experience in the midst of it all that is millions of times better than that of quiet sitting. Whenever you encounter people making a commotion, whether it concerns you or not, use it to polish and strengthen yourself, like gold being refined over and over until it no longer changes color. If you gain power in this, it is much better than long drawn-out practice in quietude.
Is there a better time to practice settling the internal storm than when faced with a bouncing dog or one who is spinning waiting for her food bowl to be put down? Most people think a dog’s nutty behavior is a nuisance. Maybe it’s just Doggie Daoism.