The point isn't what we teach dogs, it is what dogs teach us.
Excerpt from "How Animals Talk" by William Long:
"Just to take a walk with your dog may be a revelation to you, as most simple matters are when you dare to view them for yourself without prejudice. In fact, what is any revelation or discovery but seeing things as they are?
This daily walk over familiar ground, which bores you because you must take it for exercise, leaving out of it the fun which is the essential element of any exercise, is to your dog another joyous and expectant exploration of the Indes. He explored the same ground yesterday, to be sure, but all sorts of revolutions and migrations take place overnight; and if he be a real dog, not a spoiled pet, he will uncover more surprises on the familiar road than you uncover in the morning newspaper.
Follow him sympathetically as he finds endlessly interesting things where you find little but boredom, and you may learn that there are three marked differences between you and a normal animal: first, that he keeps the spirit of play, which you have well-nigh lost; second, that he lives in his sensations and is happy, while you dwell mostly in your thoughts and postpone happiness for the future; and third, that he is alive now, every moment, and you used to be alive the day before yesterday."