30 As to the subjection, there are other facts which come to the help of our faith, and prevent us from putting an indignity on Christ upon this score, but above all this passage contains its own defence. First, however, I appeal to common reason: is the subjection still to be understood as the subordination of servitude to lordship, weakness to power, meanness to honour, qualities the opposite of one another? Is the Son in this manner subjected to the Father by the distinction of a different nature?
If, indeed, we would think so, we shall find in the Apostle's words a preventive for such errors of the imagination. When all things are subjected to Him, says He, then must He be subjected to Him, Who subjects all things to Himself; and by this 'then' he means to denote the temporal Dispensation. For if we put any other construction on the subjection, Christ, though then to be subjected, is not subjected now, and thus we make Him an insolent and impious rebel, whom the necessity of time, breaking as it were and subduing His profane and overweening pride, will reduce to a tardy obedience.
But what does He Himself say? I am not come to do My own will, but the will of Him that sent Me: and again, Therefore has the Father loved Me because I do all things that are pleasing unto Him: and, Father, Your will be done. Or hear the Apostle, He humbled Himself, becoming obedient even unto death. Although He humbled Himself, His nature knew no humiliation: though He was obedient, it was a voluntary obedience, for He became obedient by humbling Himself.
The Only-begotten God humbled Himself, and obeyed His Father even to the death of the Cross: but as what, as man or as God, is He to be subjected to the Father, when all things have been subjected to Him? Of a truth this subjection is no sign of a fresh obedience, but the Dispensation of the Mystery, for the allegiance is eternal, the subjection an event within time. The subjection is then in its signification simply a demonstration of the Mystery.
Source: On the Trinity (New Advent)