Well, then, there is no argument.
But that does not tell me why the Catholics then need the Limbo. We are to be judged for that which we have done. The unbaptized infants had done nothing to be judged for, nor anything to repent for. Do you not think that God in his infinite love for humanity can not find room for Grace for unbaptized infants if he can save repentant murderers? Better yet, why speculate and confuse, as if we really know the essence of God's salvation?!
He saves repentant murderes here, on earth, if they repent. Infants do not have that opportunity nor do they need to repent - yet they are born with sin, the sin of Adam. Since death is the result of sin, if they were without sin, they would have never died in the first place.
Perhaps He can find room in heaven for unbaptised infants - perhaps He cannot. Do you believe that God allows those who have sin on their souls into heaven? We do not.
We believe there may be some middle place we call Limbo because while the unbaptised infants are not guilty of actual sin, they do have the sin of Adam on their soul. The *only* way to remove that particular sin, so far as has been revealed, is through Baptism that Christ commanded we all must have or no one gets into heaven - he did not leave a proviso for infants.
God could save unbaptized infants, but He has not chosen to reveal to us that He will or does do this. But instead He has said strictly that Baptism is absolutely necessary for salvation. This would tend to lead one to believe that He does not do so.
As I mentioned, Limbo is a speculative theological venture first broached in the written record by a Greek Father, St. Gregory Nazianz, in his Oration on Baptism; not by a Latin.
Limbo, as developed from this original strain of thought by St. Thomas Aquinas, is in fact a very loving doctrine which takes into account both the mercy and justice of God, and the necessity of Baptismal grace for achieving the beatific vision. I would encourage you to read his entire article in the Summa here:
http://www.newadvent.org/summa/600102.htm
A few short excerpts of the more important thoughts.
"... they will know perfectly things subject to natural knowledge, and both the fact of their being deprived of eternal life and the reason for this privation, and that nevertheless this knowledge will not cause any sorrow in them. ..."I say, then, that every man who has the use of free-will is adapted to obtain eternal life, because he can prepare himself for grace whereby to merit eternal life [Cf. I-II, 109, 5 and 6]; so that if he fail in this, his grief will be very great, since he has lost what he was able to possess. But children were never adapted to possess eternal life, since neither was this due to them by virtue of their natural principles, for it surpasses the entire faculty of nature, nor could they perform acts of their own whereby to obtain so great a good. Hence they will nowise grieve for being deprived of the divine vision; nay, rather will they rejoice for that they will have a large share of God's goodness and their own natural perfections. Nor can it be said that they were adapted to obtain eternal life, not indeed by their own action, but by the actions of others around them, since they could be baptized by others, like other children of the same condition who have been baptized and obtained eternal life: for this is of superabundant grace that one should be rewarded without any act of one's own. Wherefore the lack of such a grace will not cause sorrow in children who die without Baptism, any more than the lack of many graces accorded to others of the same condition makes a wise man to grieve. ...
"Although unbaptized children are separated from God as regards the union of glory, they are not utterly separated from Him: in fact they are united to Him by their share of natural goods, and so will also be able to rejoice in Him by their natural knowledge and love."
Throughout all of this, one must realize that there are not really seperate "places" of Heaven and Hell (which includes Limbo), but rather that these are seperate conditions of men after their judgement, all of whom continue to exist directly in the presence of God. Apocalypse 14.10 says the damned "shall be tormented with fire and brimstone in the sight of the holy angels and in the sight of the Lamb." And of the blessed Apocalypse 22.4 says "they shall see his face."
Basically, the damned are those who are unprepared to come face-to-face with the glory of God, and this glory meets them as a burning torment, while the just are those who are prepared, and they rejoice in the vision of His glory forever. The little children in Limbo would then be among the damned who cannot see the glory of God because they do not have the eyes of faith, yet they will not be tormented by this loss in any way, because they have no committed no sin, instead God will share His goodness with them as far as they are able naturally to comprehend and enjoy.
If that is the case, what need did we have for Jesus Christ?
Is not in your Church Jesus the Christ called the "lamb of God" because He took the place of the sacrifice of the lambs? Why did mankind need the lambs or the perfect sacrifice of Jesus if not to appease a God that was angry at us? So much for Gods infinite love.
And did not Jesus tell us that we must be born again with water and the Spirit? So there were conditions attached with His saving Grace.
Why have conditions if there are no consequences? What would be the consequence of not being born again of water, as we were instructed? Well, we couldn't enter Heaven, just as Jesus said. We are only taking Him at His word.
But if we can't enter Heaven, what to do with those who never sinned? If there is no Limbo, then there is only one other possibility.
So while it's possible there is no Limbo, wouldn't we at least feel better thinkng there is one? The concept should at least be understandable, even if you don't believe it.
Luckily it does not matter what you and I believe, and our understanding does not affect God's decisions.