IV. The reason explained why Easter and Whitsuntide are the proper seasons for baptism.
Although, therefore, both these things which are connected with Christ's humiliation and those which are connected with His exaltation meet in one and the same Person, and all that is in Him of Divine power and human weakness conduces to the accomplishment of our restoration: yet it is appropriate that the power of baptism should change the old into the new creature on the death-day of the Crucified and the Resurrection-day of the Dead: that Christ's death and His resurrection may operate in the re-born, as the blessed Apostle says: “Are you ignorant that all we who were baptized in Christ Jesus, were baptized in His death?
We were buried with Him through baptism into death; that as Christ rose from the dead through the glory of the Father, so we also should walk in newness of life. For if we have become united with the likeness of His death, we shall be also (with the likeness) of His resurrection,” and the rest which the Teacher of the Gentiles discusses further in recommending the sacrament of baptism: that it might be seen from the spirit of this doctrine that that is the day, and that the time chosen for regenerating the sons of men and adopting them among the sons of God, on which by a mystical symbolism and form, what is done in the limbs coincides with what was done in the Head Himself, for in the baptismal office death ensues through the slaying of sin, and threefold immersion imitates the lying in the tomb three days, and the raising out of the water is like Him that rose again from the tomb. The very nature, therefore of the act teaches us that that is the recognized day for the general reception of the grace, on which the power of the gift and the character of the action originated.
And this is strongly corroborated by the consideration that the Lord Jesus Christ Himself, after He rose from the dead, handed on both the form and power of baptizing to His disciples, in whose person all the chiefs of the churches received their instructions with these words, “Go and teach all nations, baptizing them in the name of the Father and of the Son and of the Holy Ghost.” On which of course He might have instructed them even before His passion, had He not especially wished it to be understood that the grace of regeneration began with His resurrection.
It must be added, indeed, that the solemn season of Pentecost, hallowed by the coming of the Holy Ghost is also allowed, being as it were, the sequel and completion of the Paschal feast. And while other festivals are held on other days of the week, this festival (of Pentecost) always occurs on that day, which is marked by the Lord's resurrection: holding out, so to say, the hand of assisting grace and inviting those, who have been cut off from the Easter feast by disabling sickness or length of journey or difficulties of sailing, to gain the purpose that they long for through the gift of the Holy Spirit.
For the Only-begotten of God Himself wished no difference to be felt between Himself and the Holy Spirit in the Faith of believers and in the efficacy of His works: because there is no diversity in their nature, as He says, “I will ask the Father and He shall give you another Comforter that He may be with you for ever, even the Spirit of Truth;” and again: “But the Comforter which is the Holy Ghost, whom the Father will send in My name, He shall teach you all things and bring to your remembrance all that I said unto you;” and again: “When He, the Spirit of Truth, has come, He shall guide you into all the Truth.”
And thus, since Christ is the Truth, and the Holy Spirit the Spirit of Truth, and the name of “Comforter” appropriate to both, the two festivals are not dissimilar, where the sacrament is the same.
Source: Letters (New Advent)