Prior to working for my previous boss, I wasn't very good at my work. Consequently, I wasn't very confident, and was rather passive-aggressive and indecisive. Once my boss hired me and began to train me, I became more confident and decisive.
The first thing he trained me to do was paint sharp lines. His business was predicated on provided the highest quality painting service, and to that end the first goal of every job was to make our work look as clean and crisp as possible.
The second thing he trained me to do was clean up messes. If the first thing customer's notice is sloppy lines, the second thing they notice are messy floors. To that end, I was expected to take precautions to avoid making messes, then go back and clean up when the work was done.
After that, he taught me how to talk to customers, how to manage job sites, and how to attend to various details that make customers want to hire you again. In providing me with a set of values, he enabled me to focus my decision-making. By taking responsibility for his rules, he gave me confidence to act decisively.
Thus, I learned that submission brings to itself its own type of authority. Submitting to an authority gives you a paradigm in which to operate, thus focusing your work and making you more decisive. Certain options are removed from before you simply because they do not fit within the framework provided by the one to whom you submit. Furthermore, you can be confident in your decisions because, in a sense, you aren't really the one making them.
Paradoxically, submission brings forth a strong sense of authority because it gives you a framework for decisions. The decision-making framework provides a goal and limits one's options. Consequently, one can make decisions more quickly and confidently because one doesn't have to do any first-order thinking or parse through as many second-order options. Thus, the reason why submission to a higher authority makes one seem more authoritative is because submission to a higher authority makes one a lower authority, extrapolating a paradigm downward.