In the dog world, the leader always goes first. A dog who races to the door ahead of his owner is showing disrespect, and doesn’t see the human as the alpha of his pack. -- Unattributed out of respect to your brain function.
When I read the above quote and I think about how I never conditioned Riley to wait for me to go outside before him and of all the dogs I walk on a daily basis as a dog walker that go out the door first so I can close it behind us I never once think it is disrespectful. Like a lot of dogs Riley loves going outside. Being outside is one of his favorite things to do. There are times when it's cold and rainy and miserable and I just want to go inside that I start to wonder if Riley is malfunctioning and can't feel the harsh weather but the reality is he just loves being outside that much. When Riley gets the opportunity to go outside he is going to take it and he is very likely going out the door ahead of me not because he doesn't respect me but because he is excited to be outside.
When this type of thinking is applied to dogs it creates in me a couple questions. The first is I wonder if respect is an emotion and if it is controlled by the endocrine system or if it is a human concept and therefor meaningless to dogs. The second is I want to question the people that believe dogs understand the concept of respect how much respect they have for the emotional state of dogs. Dogs have been shown to show complex emotions like depression and jealousy but my guess is those that talk about dogs needing to respect humans as their master would not credit dogs with the ability to feel these higher emotions.
I also understand that my disrespect for the word respect might come from my own background. Think of the people in your life that have told you that respect is earned not given. These tend to be people that fit more into the category of a bully and want you to respect them and use the concept of respect as a manipulation tool to get you to do things for them in order to earn their respect while never truly respecting you or your agency as a human being. When I think of the people I respect it is those that view me as an equal. If I feel disrespected or slighted by someone I don't try and earn their respect I just stop respecting them. Wielding the concept of respect as a way to gain authoritarian control over another human being or a dog is a much better way to be feared than respected. In our human interactions those that we respect are people that command but never demand respect and those that do demand respect I wonder if they even have an idea of what it means.
By the way respect is defined as a feeling of deep admiration for someone elicited by the abilities, qualities, or achievements. By the very definition of respect the quote that proceeded this post isn't talking at all about respect. Your dog can admire you and admire you deeply enough to feel what a human would call respect and simultaneously be excited to go outside and so excited that they run out the door as soon as it is opened without waiting for you.
My view of the dog/human relationship is that it is one of companionship and compassion founded on love, trust, and understanding and not a relationship where one partner is submissive to the other, and honestly unless your name is Christian Grey you would not view the latter as a healthy relationship. In other words if you want your dog to respect you first work on building a relationship built on love, trust, and understanding because, after all, respect is a deep feeling of admiration.