|Dante in the Limbo of the Poets|
It is one of those "was it really a teaching" items that has fallen by the wayside, that cannot be proven from ancient writings, but which gained a substantial following because of its intellectual consistency and approached the status of doctrine in the minds of some. I am, of course, speaking of Limbo.
What is it? There are usually two answers. One is that it is an alternative to heaven and hell for the invincibly and inculpably ignorant children who died before reaching the age of reason. Another is a variation, that it is a painless part of hell for those same dead, who will live in a "state of perfect natural happiness" in the eternal abyss. It is distinct from the "Limbo of the Fathers," or the Greek "Hades," where the righteous of the Old Covenant dwelt after death until Christ freed them on Holy Saturday.
Some will gerrymander patristic quotations from the likes of St. Gregory the Theologian, who believed that those who innocently died without Baptism did not merit punishment, to support Limbo (cf. Orat. XL). The general patristic consensus in the Greek Church reflects Gregory's misgivings and agnosticism on the subject.
St. Augustine informed the older Western view, that the un-baptized, regardless of who they are, go to hell and suffer. Rereading Augustine's Confessions barrels the reader in amazement at his own guilt for crying and waling as a child, and in turn believing that other babies sinned by selfishly crying and waling (cf. ch. 2).
Proto-Scholastics, St. Anslem and his descendants, applied logic to the disparity between the guilt of infants and their fallen state, concluding that they must earn some sort of separation from God that does not involve suffering, although one would think any separation from God is a pain. Aquinas would write about Limbo, but Limbo itself would not grasp the Catholic imagination outside of the academies for quite some time. In his Inferno, Dante imagines the first ring to encapsulate Virgil and other virtuous pagans who, without illumination from faith, must suffer separation from God, but who themselves did not deserve punishment.
Eventually, Limbo caught on until Benedict XVI "closed" it in 2007 with this document, which suggests all un-baptized infants might be saved. While the conclusion is not out of the realm of possibility, given the patristic Greek agnosticism on the subject, it boldly disregards the Latin tradition on the subject. Moreover, there a curious application of lex orandi lex credendi: the old rite did not have a funeral rite for un-baptized infants, but the new rite does, so we can assume....
There is nothing wrong necessarily with holding a funeral for an un-baptized infant who would have been washed in the cleansing waters. The Church makes that very accommodation for prematurely deceased catechumens. I just which we would stop trying to find as answer to everything. Who gets to go to heaven or hell is inevitably up to God, the Only One qualified for His position, not theologians. This is not a criminal mystery to be solved by detectives, it is a mystery of faith to be left alone by the faithful. We do not know and may not until eternity. Why is this so difficult?