Can. 3. It has been decided likewise that if anyone says that for this reason the Lord said: "In my Father's house there are many mansions": that it might be understood that in the kingdom of heaven there will be some middle place or some place anywhere where the blessed infants live who departed from this life without baptism, without which they cannot enter into the kingdom of heaven, which is life eternal, let him be anathema. For when the Lord says: "Unless a man be born again of water and the Holy Ghost, he shall not enter into the kingdom of God", what Catholic will doubt that he will be a partner of the devil who has not deserved to be a coheir of Christ? For he who lacks the right part will without doubt run into the left. (Council of Mileum II, 416)
It (The Roman Church) teaches ... that the souls ... of those who die in mortal sin, or with only original sin descend immediately into hell; however, to be punished with different penalties and in different places. (Pope John XXII, Letter "Nequaquam sine dolere", To the Armenians, Nov. 21, 1321)
If what We have said up to now concerns the protection and care of natural life, much more so must it concern the supernatural life, which the newly born receives with Baptism. In the present economy there is no other way to communicate that life to the child who has not attained the use of reason. Above all, the state of grace is absolutely necessary at the moment of death without it salvation and supernatural happiness—the beatific vision of God—are impossible. An act of love is sufficient for the adult to obtain sanctifying grace and to supply the lack of baptism; to the still unborn or newly born this way is not open. Therefore, if it is considered that charity to our fellowman obliges us to assist him in the case of necessity, then this obligation is so much the more important and urgent as the good to be obtained or the evil to be avoided is the greater, and in the measure that the needy person is incapable of helping or saving himself with his own powers; and so it is easy to understand the great importance of providing for the baptism of the child deprived of complete reason who finds himself in grave danger or at death's threshold. (Pius XII, Allocution to Midwives, Oct. 29, 1951)
The puzzlement here, at least between the Orthodox and the Augustinians, was about the nature of Original Sin and the effects of that nature. To understand those, and in particular, to avoid a caricature of Catholicism that we saw on occasion on this thread, one must study the post-Augustinian teaching.