Objection 1. It would seem that spiritual relationship is not contracted between the person baptized and the person who raises him from the sacred font. For in carnal generation carnal relationship is contracted only on the part of the person of whose seed the child is born; and not on the part of the person who receives the child after birth. Therefore neither is spiritual relationship contracted between the receiver and the received at the sacred font.
Objection 2. Further, he who raises a person from the sacred font is called anadochos by Dionysius (Eccl. Hier. ii): and it is part of his office to instruct the child. But instruction is not a sufficient cause of spiritual relationship, as stated above (Article 2). Therefore no relationship is contracted between him and the person whom he raises from the sacred font.
Objection 3. Further, it may happen that someone raises a person from the sacred font before he himself is baptized. Now spiritual relationship is not contracted in such a case, since one who is not baptized is not capable of spirituality. Therefore raising a person from the sacred font is not sufficient to contract a spiritual relationship.
On the contrary, There is the definition of spiritual relationship quoted above (Article 1), as also the authorities mentioned in the text (Sent. iv, D, 42).
I answer that, Just as in carnal generation a person is born of a father and mother, so in spiritual generation a person is born again a son of God as Father, and of the Church as Mother. Now while he who confers the sacrament stands in the place of God, whose instrument and minister he is, he who raises a baptized person from the sacred font, or holds the candidate for Confirmation, stands in the place of the Church. Therefore spiritual relationship is contracted with both.
Reply to Objection 1. Not only the father, of whose seed the child is born, is related carnally to the child, but also the mother who provides the matter, and in whose womb the child is begotten. So too the godparent who in place of the Church offers and raises the candidate for Baptism and holds the candidate for Confirmation contracts spiritual relationship.
Reply to Objection 2. He contracts spiritual relationship not by reason of the instruction it is his duty to give, but on account of the spiritual birth in which he co-operates.
Reply to Objection 3. A person who is not baptized cannot raise anyone from the sacred font, since he is not a member of the Church whom the godparent in Baptism represents: although he can baptize, because he is a creature of God Whom the baptizer represents. And yet he cannot contract a spiritual relationship, since he is void of spiritual life to which man is first born by receiving Baptism.
Source: Summa Theologica (New Advent)