Objection 1. It seems that in Baptism it is not necessary for someone to raise the baptized from the sacred font. For our Baptism is consecrated by Christ's Baptism and is conformed thereto. But Christ when baptized was not raised by anyone from the font, but according to Matthew 3:16, "Jesus being baptized, forthwith came out of the water." Therefore it seems that neither when others are baptized should anyone raise the baptized from the sacred font.
Objection 2. Further, Baptism is a spiritual regeneration, as stated above (Article 3). But in carnal generation nothing else is required but the active principle, i.e. the father, and the passive principle, i.e. the mother. Since, then, in Baptism he that baptizes takes the place of the father, while the very water of Baptism takes the place of the mother, as Augustine says in a sermon on the Epiphany (cxxxv); it seems that there is no further need for someone to raise the baptized from the sacred font.
Objection 3. Further, nothing ridiculous should be observed in the sacraments of the Church. But it seems ridiculous that after being baptized, adults who can stand up of themselves and leave the sacred font, should be held up by another. Therefore there seems no need for anyone, especially in the Baptism of adults, to raise the baptized from the sacred font.
On the contrary, Dionysius says (Eccl. Hier. ii) that "the priests taking the baptized hand him over to his sponsor and guide."
I answer that, The spiritual regeneration, which takes place in Baptism, is in a certain manner likened to carnal generation: wherefore it is written (1 Peter 2:2): "As new-born babes, endowed with reason desire milk [Vulgate: 'desire reasonable milk'] without guile." Now, in carnal generation the new-born child needs nourishment and guidance: wherefore, in spiritual generation also, someone is needed to undertake the office of nurse and tutor by forming and instructing one who is yet a novice in the Faith, concerning things pertaining to Christian faith and mode of life, which the clergy have not the leisure to do through being busy with watching over the people generally: because little children and novices need more than ordinary care. Consequently someone is needed to receive the baptized from the sacred font as though for the purpose of instructing and guiding them. It is to this that Dionysius refers (Eccl. Hier. xi) saying: "It occurred to our heavenly guides," i.e. the Apostles, "and they decided, that infants should be taken charge of thus: that the parents of the child should hand it over to some instructor versed in holy things, who would thenceforth take charge of the child, and be to it a spiritual father and a guide in the road of salvation."
Reply to Objection 1. Christ was baptized not that He might be regenerated, but that He might regenerate others: wherefore after His Baptism He needed no tutor like other children.
Reply to Objection 2. In carnal generation nothing is essential besides a father and a mother: yet to ease the latter in her travail, there is need for a midwife; and for the child to be suitably brought up there is need for a nurse and a tutor: while their place is taken in Baptism by him who raises the child from the sacred font. Consequently this is not essential to the sacrament, and in a case of necessity one alone can baptize with water.
Reply to Objection 3. It is not on account of bodily weakness that the baptized is raised from the sacred font by the godparent, but on account of spiritual weakness, as stated above.
Source: Summa Theologica (New Advent)