A child's obedience
Col. 3:20: Children, be obedient to your parents in all things, for this is well-pleasing to the Lord (NASU).
Kids should obey their parents for lots of reasons, but one is because obedience maintains the divinely ordained order in the home. There must be a person in charge. But, that does not imply that the parent is more or less important to the household. It only means they have the final authority to which everyone else should lovingly submit.
Authority is an interesting concept. It has much more to do with order than it does with value or ability. A private in the army can be a more valuable or able soldier without having a higher rank than his commanding officer. The officer has more authority, but that does not make him a better man. He earns the respect of his men by executing his authority in a Christ-like way.
Children should submit to their parents because God has given parents authority—to raise, nurture, guide and discipline them in love. But, submission is not the same as defeat.
"Submission" recognizes God's order for the home and joyfully obeys parents who are worthy of it.