That is why I did not even consider myself worthy to come to you. But say the word, and my servant will be healed. For I myself am a man under authority, with soldiers under me. He doesn't have to do it himself in person. Parents learn gradually to assign chores to their children to get the housework done.
Office managers organize the staff to accomplish the work.
An Army captain assigns a lieutenant a mission to accomplish under the captain's orders. And the lieutenant issues orders to the sergeant, who, in turn, issues orders to his own men. Each man in the chain of command is acting under orders from above. And with the responsibility to fulfill the order also comes the authority to accomplish it by whatever authorized means are necessary. The centurion sees Jesus as a commander like himself.