Objection 1. It would seem that it was not fitting that Christ should die. For a first principle in any order is not affected by anything contrary to such order: thus fire, which is the principle of heat, can never become cold. But the Son of God is the fountain-head and principle of all life, according to Psalm 35:10: "With Thee is the fountain of life." Therefore it does not seem fitting for Christ to die.
Objection 2. Further, death is a greater defect than sickness, because it is through sickness that one comes to die. But it was not beseeming for Christ to languish from sickness, as Chrysostom [Athanasius, Orat. de Incarn. Verbi] says. Consequently, neither was it becoming for Christ to die.
Objection 3. Further, our Lord said (John 10:10): "I am come that they may have life, and may have it more abundantly." But one opposite does not lead to another. Therefore it seems that neither was it fitting for Christ to die.
On the contrary, It is written, (John 11:50): "It is expedient that one man should die for the people... that the whole nation perish not": which words were spoken prophetically by Caiphas, as the Evangelist testifies.
I answer that, It was fitting for Christ to die. First of all to satisfy for the whole human race, which was sentenced to die on account of sin, according to Genesis 2:17: "In what day soever ye shall [Vulgate: 'thou shalt'] eat of it ye shall [Vulgate: 'thou shalt'] die the death." Now it is a fitting way of satisfying for another to submit oneself to the penalty deserved by that other. And so Christ resolved to die, that by dying He might atone for us, according to 1 Peter 3:18: "Christ also died once for our sins." Secondly, in order to show the reality of the flesh assumed. For, as Eusebius says (Orat. de Laud. Constant. xv), "if, after dwelling among men Christ were suddenly to disappear from men's sight, as though shunning death, then by all men He would be likened to a phantom." Thirdly, that by dying He might deliver us from fearing death: hence it is written (Hebrews 2:14-15) that He communicated "to flesh and blood, that through death He might destroy him who had the empire of death and might deliver them who, through the fear of death, were all their lifetime subject to servitude." Fourthly, that by dying in the body to the likeness of sin--that is, to its penalty--He might set us the example of dying to sin spiritually. Hence it is written (Romans 6:10): "For in that He died to sin, He died once, but in that He liveth, He liveth unto God: so do you also reckon that you are dead to sin, but alive unto God." Fifthly, that by rising from the dead, and manifesting His power whereby He overthrew death, He might instill into us the hope of rising from the dead. Hence the Apostle says (1 Corinthians 15:12): "If Christ be preached that He rose again from the dead, how do some among you say, that there is no resurrection from the dead?"
Reply to Objection 1. Christ is the fountain of life, as God, and not as man: but He died as man, and not as God. Hence Augustine [Vigilius Tapsensis] says against Felician: "Far be it from us to suppose that Christ so felt death that He lost His life inasmuch as He is life in Himself; for, were it so, the fountain of life would have run dry. Accordingly, He experienced death by sharing in our human feeling, which of His own accord He had taken upon Himself, but He did not lose the power of His Nature, through which He gives life to all things."
Reply to Objection 2. Christ did not suffer death which comes of sickness, lest He should seem to die of necessity from exhausted nature: but He endured death inflicted from without, to which He willingly surrendered Himself, that His death might be shown to be a voluntary one.
Reply to Objection 3. One opposite does not of itself lead to the other, yet it does so indirectly at times: thus cold sometimes is the indirect cause of heat: and in this way Christ by His death brought us back to life, when by His death He destroyed our death; just as he who bears another's punishment takes such punishment away.
Source: Summa Theologica (New Advent)