Objection 1. It would seem that Christ did not die out of obedience. For obedience is referred to a command. But we do not read that Christ was commanded to suffer. Therefore He did not suffer out of obedience.
Objection 2. Further, a man is said to do from obedience what he does from necessity of precept. But Christ did not suffer necessarily, but voluntarily. Therefore He did not suffer out of obedience.
Objection 3. Further, charity is a more excellent virtue than obedience. But we read that Christ suffered out of charity, according to Ephesians 5:2: "Walk in love, as Christ also has loved us, and delivered Himself up for us." Therefore Christ's Passion ought to be ascribed rather to charity than to obedience.
On the contrary, It is written (Philippians 2:8): "He became obedient" to the Father "unto death."
I answer that, It was befitting that Christ should suffer out of obedience. First of all, because it was in keeping with human justification, that "as by the disobedience of one man, many were made sinners: so also by the obedience of one, many shall be made just," as is written Romans 5:19. Secondly, it was suitable for reconciling man with God: hence it is written (Romans 5:10): "We are reconciled to God by the death of His Son," in so far as Christ's death was a most acceptable sacrifice to God, according to Ephesians 5:2: "He delivered Himself for us an oblation and a sacrifice to God for an odor of sweetness." Now obedience is preferred to all sacrifices. according to 1 Samuel 15:22: "Obedience is better than sacrifices." Therefore it was fitting that the sacrifice of Christ's Passion and death should proceed from obedience. Thirdly, it was in keeping with His victory whereby He triumphed over death and its author; because a soldier cannot conquer unless he obey his captain. And so the Man-Christ secured the victory through being obedient to God, according to Proverbs 21:28: "An obedient man shall speak of victory."
Reply to Objection 1. Christ received a command from the Father to suffer. For it is written (John 10:18): "I have power to lay down My life, and I have power to take it up again: (and) this commandment have I received of My Father"--namely, of laying down His life and of resuming it again. "From which," as Chrysostom says (Hom. lix in Joan.), it is not to be understood "that at first He awaited the command, and that He had need to be told, but He showed the proceeding to be a voluntary one, and destroyed suspicion of opposition" to the Father. Yet because the Old Law was ended by Christ's death, according to His dying words, "It is consummated" (John 19:30), it may be understood that by His suffering He fulfilled all the precepts of the Old Law. He fulfilled those of the moral order which are founded on the precepts of charity, inasmuch as He suffered both out of love of the Father, according to John 14:31: "That the world may know that I love the Father, and as the Father hath given Me commandment, so do I: arise, let us go hence"--namely, to the place of His Passion: and out of love of His neighbor, according to Galatians 2:20: "He loved me, and delivered Himself up for me." Christ likewise by His Passion fulfilled the ceremonial precepts of the Law, which are chiefly ordained for sacrifices and oblations, in so far as all the ancient sacrifices were figures of that true sacrifice which the dying Christ offered for us. Hence it is written (Colossians 2:16-17): "Let no man judge you in meat or drink, or in respect of a festival day, or of the new moon, or of the sabbaths, which are a shadow of things to come, but the body is Christ's," for the reason that Christ is compared to them as a body is to a shadow. Christ also by His Passion fulfilled the judicial precepts of the Law, which are chiefly ordained for making compensation to them who have suffered wrong, since, as is written Psalm 68:5: He "paid that which" He "took not away," suffering Himself to be fastened to a tree on account of the apple which man had plucked from the tree against God's command.
Reply to Objection 2. Although obedience implies necessity with regard to the thing commanded, nevertheless it implies free-will with regard to the fulfilling of the precept. And, indeed, such was Christ's obedience, for, although His Passion and death, considered in themselves, were repugnant to the natural will, yet Christ resolved to fulfill God's will with respect to the same, according to Psalm 39:9: "That I should do Thy will: O my God, I have desired it." Hence He said (Matthew 26:42): "If this chalice may not pass away, but I must drink it, Thy will be done."
Reply to Objection 3. For the same reason Christ suffered out of charity and out of obedience; because He fulfilled even the precepts of charity out of obedience only; and was obedient, out of love, to the Father's command.
Source: Summa Theologica (New Advent)