1) Myth - If your dog exits the doorway ahead of you, he/she is being dominant.
The Reality - This idea started with the notion that the alpha wolves led the pack and if you wanted to be a "pack leader" you need to walk ahead of your dog. The alpha dog concept has been questioned in recent years as scholars have argued that the old studies on captive wolves do not reflect what goes on in wild populations. Moreover, dog social structures seem to be more fluid and less hierarchical than wolf populations. For a more detailed explanation and list scientific sources, read my article on the alpha dog theory. The simple explanation for dogs wanting to run out the door is that what is outside is much more interesting than what they see inside the house day after day. Walks are really rewarding for dogs, mentally and physcially, so it is no surprise that they want to run out the door.
The main reason to train a dog to wait behind a door before you release them for the walk is for safety not to show your "dominance" over the dog. You don't want a dog make a habit of charging out of a door, especially if the leash has not been securely fastened.
Because going for a walk is what I call a "life reward," I use this fact to my advantage and ask the dog to perform a behavior such as a "sit" or "wait" before I open the door and let them outside. By doing this, I reinforce their training (sit and wait) and the great thing is that the reward is not food, but the walk itself.
2) Myth - A dog that walks ahead of you on a walk is being dominant.
The Reality - again, this notion has its roots in dominance or alpha dog theories and like the doorway myth, the studies do not support this idea. I think the simplest explanation as to why dogs like to forge ahead on walks is because they usually can walk faster than us and what is in front of us is much more interesting. It is not so much about controlling you as it is excitement and trying to burn off some mental and physical energy. Walks are very exciting for dogs and are often the highlight of a dog's day. I advocate the notion of walking with a loose leash which is comfortable for both the dog and owner. A dog that is pulling you with a taut leash or a dog that zig zags is simply an untrained dog.
If you have a leash aggressive dog, however, you may want to train your dog to walk closer to you because giving an aggressive dog too much space ahead of you makes it harder for you to control and work with your dog if he/she becomes reactive when he/she sees another dog or person. Again, keeping a dog closer to you in this scenario is more for safety and training purposes rather than rooted in notions of your dog trying to dominate you.
3) Myth - Your dog should not be allowed sniff the ground on walks.
The Reality - this one makes me sad and I am not sure how this idea got started. It causes owners (and the dog) a lot of undue stress and owners often end up jerking the dog around in frustration. The highlight of a dog's day is to be able to smell the "calling card" left by other dogs and leave one himself/herself. A dog's sense of smell is so sharp compared to ours that there is a lot of information picked up by smelling the ground. It is also good mental stimulation as your dog is processing information about the neighborhood. When dogs are young puppies, I feel that smelling the world is vitally important for their development and learning not to fear the world outside the home. Jerking on a puppy's collar every time he/she tried to investigate the world is very stressful and makes a walk unpleasant for the dog.
In a casual walk, I allow my dogs to smells things and they manage to keep walking with me in a straight line and on a loose lead. Akitas and shibas were bred for hunting and I am not going to deny them the pleasure of smelling things. Moreover, my dogs do not need to look up at me adoringly for our entire 45 minute walk. I am not training them for competitive obedience and neither are 99% of average dog owners. If my dog lingers too long at a spot or if we need to keep moving, I have a verbal cue "let's go" and she knows that we need to move on. If I need to her to go to a heel position and focus on staying close to me I have a verbal cue "heel." But, the bulk of my walks are leisurely, loose leash walks and keeping a strict heel for the entire walk is not necessary. My view is that when I attach a leash to my dog, the walk around the neighborhood is for her pleasure just as much as mine. Would you go on a hike without admiring the scenery? Well, going on a walk without being able to smell things would be the equivalent deprivation for a dog.
Now if your dog is zig zagging back and forth or pulling you around to smell something, that is an issue of training your dog to walk in a straight line without pulling. This is a separate issue from letting your dog smell things once in awhile on a walk.
So, next time you go for a walk, enjoy the sights and sounds. Stop and smell the roses (or in the case of your dog, the hydrant).
Los Angeles Dog Trainer