Objection 1. It seems that he who raises anyone from the sacred font is not bound to instruct him. For none but those who are themselves instructed can give instruction. But even the uneducated and ill-instructed are allowed to raise people from the sacred font. Therefore he who raises a baptized person from the font is not bound to instruct him.
Objection 2. Further, a son is instructed by his father better than by a stranger: for, as the Philosopher says (Ethic. viii), a son receives from his father, "being, food, and education." If, therefore, godparents are bound to instruct their godchildren, it would be fitting for the carnal father, rather than another, to be the godparent of his own child. And yet this seems to be forbidden, as may be seen in the Decretals (xxx, qu. 1, Cap. Pervenit and Dictum est).
Objection 3. Further, it is better for several to instruct than for one only. If, therefore, godparents are bound to instruct their godchildren, it would be better to have several godparents than only one. Yet this is forbidden in a decree of Pope Leo, who says: "A child should not have more than one godparent, be this a man or a woman."
On the contrary, Augustine says in a sermon for Easter (clxviii): "In the first place I admonish you, both men and women, who have raised children in Baptism, that ye stand before God as sureties for those whom you have been seen to raise from the sacred font."
I answer that, Every man is bound to fulfil those duties which he has undertaken to perform. Now it has been stated above (Article 7) that godparents take upon themselves the duties of a tutor. Consequently they are bound to watch over their godchildren when there is need for them to do so: for instance when and where children are brought up among unbelievers. But if they are brought up among Catholic Christians, the godparents may well be excused from this responsibility, since it may be presumed that the children will be carefully instructed by their parents. If, however, they perceive in any way that the contrary is the case, they would be bound, as far as they are able, to see to the spiritual welfare of their godchildren.
Reply to Objection 1. Where the danger is imminent, the godparent, as Dionysius says (Eccl. Hier. vii), should be someone "versed in holy things." But where the danger is not imminent, by reason of the children being brought up among Catholics, anyone is admitted to this position, because the things pertaining to the Christian rule of life and faith are known openly by all. Nevertheless an unbaptized person cannot be a godparent, as was decreed in the Council of Mainz, although an unbaptized person: because the person baptizing is essential to the sacrament, wherefore as the godparent is not, as stated above (7, ad 2).
Reply to Objection 2. Just as spiritual generation is distinct from carnal generation, so is spiritual education distinct from that of the body; according to Hebrews 12:9: "Moreover we have had fathers of our flesh for instructors, and we reverenced them: shall we not much more obey the Father of Spirits, and live?" Therefore the spiritual father should be distinct from the carnal father, unless necessity demanded otherwise.
Reply to Objection 3. Education would be full of confusion if there were more than one head instructor. Wherefore there should be one principal sponsor in Baptism: but others can be allowed as assistants.
Source: Summa Theologica (New Advent)