Objection 1. It seems that one man is not bound to obey another. For nothing should be done contrary to the divine ordinance. Now God has so ordered that man is ruled by his own counsel, according to Sirach 15:14, "God made man from the beginning, and left him in the hand of his own counsel." Therefore one man is not bound to obey another.
Objection 2. Further, if one man were bound to obey another, he would have to look upon the will of the person commanding him, as being his rule of conduct. Now God's will alone, which is always right, is a rule of human conduct. Therefore man is bound to obey none but God.
Objection 3. Further, the more gratuitous the service the more is it acceptable. Now what a man does out of duty is not gratuitous. Therefore if a man were bound in duty to obey others in doing good deeds, for this very reason his good deeds would be rendered less acceptable through being done out of obedience. Therefore one man is not bound to obey another.
On the contrary, It is prescribed (Hebrews 13:17): "Obey your prelates and be subject to them."
I answer that, Just as the actions of natural things proceed from natural powers, so do human actions proceed from the human will. On natural things it behooved the higher to move the lower to their actions by the excellence of the natural power bestowed on them by God: and so in human affairs also the higher must move the lower by their will in virtue of a divinely established authority. Now to move by reason and will is to command. Wherefore just as in virtue of the divinely established natural order the lower natural things need to be subject to the movement of the higher, so too in human affairs, in virtue of the order of natural and divine law, inferiors are bound to obey their superiors.
Reply to Objection 1. God left man in the hand of his own counsel, not as though it were lawful to him to do whatever he will, but because, unlike irrational creatures, he is not compelled by natural necessity to do what he ought to do, but is left the free choice proceeding from his own counsel. And just as he has to proceed on his own counsel in doing other things, so too has he in the point of obeying his superiors. For Gregory says (Moral. xxxv), "When we humbly give way to another's voice, we overcome ourselves in our own hearts."
Reply to Objection 2. The will of God is the first rule whereby all rational wills are regulated: and to this rule one will approaches more than another, according to a divinely appointed order. Hence the will of the one man who issues a command may be as a second rule to the will of this other man who obeys him.
Reply to Objection 3. A thing may be deemed gratuitous in two ways. On one way on the part of the deed itself, because, to wit, one is not bound to do it; in another way, on the part of the doer, because he does it of his own free will. Now a deed is rendered virtuous, praiseworthy and meritorious, chiefly according as it proceeds from the will. Wherefore although obedience be a duty, if one obey with a prompt will, one's merit is not for that reason diminished, especially before God, Who sees not only the outward deed, but also the inward will.
Source: Summa Theologica (New Advent)