Subordination:
1. The act of subordinating, subjecting, or placing in a lower order, rank, or position, or in proper degrees of rank; also, the state of being subordinate or inferior; inferiority of rank or dignity.
2. Degree of lesser rank.
3. The state of being under control of government; subjection to rule; habit of obedience to orders.
4. The act of subordinating, placing in a lower order, or subjecting.
5. The quality or state of being subordinate or inferior to an other; inferiority of rank or dignity; subjection.
6. Place of inferior rank.
7. The process of making something subordinate.
8. The property of being subordinate.
9. The quality of being properly obedient to a superior (as a superior officer).
As you see when you expect your dog to be obedient your are placing yourself on a higher rank, so your dog is your subordinate.
When you expect your employee to be subordinate your are expecting him to obey when something is asked or tasked from ranks higher than their's in your organization. Your are also expecting him to obey to what is written in the subordination contract signed by both.
Wikipedia: obedience, in human behavior, is a form of "social influence in which a person yields to explicit instructions or orders from an authority figure".
What I think to be the main issue is the word "order". IMHO an order is not something that might exist in a workplace, with few exceptions. Your boss gives you tasks and expect you to execute them remaining inside a more or less explicit set of rules, your boss cannot give you orders.