Every man is given sufficient grace to save his soul. I have read some of the Fathers who say that the antichrist, when he comes, will be given actual graces, which he will of course reject. One of the theologians said that the antichrist will even have a guardian angel who will try and help him to save his soul, but to no avail.
Fr. Wathen told us, "God sends no man to hell, a man sends himself to hell." It is a mystery why some infants die without baptism, but let us face the fact, had they gone on to lead adult lives they would have had a deeper place in hell more than likely.
I'm not sure I buy this formula, as it appears too simplistic. How about an infant who dies without the Sacrament of Baptism? Sometimes these formulas "sound good" and are adopted, just like the misapplied SSPX formula "faith is greater than obedience" ... sounds good on the surface, but completely misapplied to the papal teaching authority.
In any case, it is true that there's no one in Hell who did not choose to go there, but salvation, elevation to the Beatific Vision is a gift owed to no man, as it's above our nature, not required in justice, etc. In the case of infants who die without Baptism, I'm sure that in many, most, if not all cases ... that was allowed to happen because God had foreknowledge that they would reject any graces that would be given him and end up in Hell, with Limbo being a great Mercy from God.
God sometimes will WITHOLD grace when He foreknows that it will be rejected. So God WOULD offer every man the graces sufficient for salvation, WERE they going to accept them, but He will sometimes withold them out of Mercy, to prevent their greater punishment for having refused them.
God WILLS that all men be saved, but He does not take away THEIR free will, and God WOULD give every man sufficient grace for salvation IF they were going to accept it.
Let's say I have $10,000 and intend to give it to my son, but I (suddenly given a gift of foreknowledge) realized that my son would take the money, buy a motorcycle with it, and kill himself. So I withold the money. I fully intended to give him the money, and I willed to give it to him, but am witholding it only due to the known outcome. There's no injustice or lack of mercy on my part to give him the money. In fact, it would be cruel and unmerciful of me to give it to him given the knowledge I have of what would happen. This does not make it so that I'm a greedy / ungenerous individual.