Some might, then, argue that God is the Father of all men by nature, even if not spiritually, but this does not follow at all. First of all, God is the Creator and author of our nature, yes, and as the Catechism of the Council of Trent teaches:
"Nam cum Deus hominem creaverit ad imaginem suam, nec illam ceteris animantibus impertiverit, ex hoc singulari munere, quo hominem ornavit, jure omnium hominum, nec fideliummodo, sed etiam infidelium, Pater in divinis scripturis appellatur."
That is to say: "Given that God has created man to His image, and has not bestowed it upon the other living creatures, on account of this unique privilege, with which He has adorned man, a right of all men, not only of the faithful, but also of infidels, in the divine Scriptures He is called Father."
It is indeed true that the faithful and the unbelieving are made in the image and likeness of God, and no amount of unbelief can remove that from them. But do not be deceived by modern corrupt translations, which allege this passage to teach that God is called the Father of unbelievers in Scripture. We have already seen seen above that such an allegation is absolutely false and indeed contrary to the Scriptures, and also contrary to the dogmatic canon of Trent quoted at the beginning of this article. It is only by adoption that can we be His sons, since we are not of God's nature. A look at an English Catechism from 1873 confirms this clear distinction between "Father" and "Creator" as separate titles. Though we may have lost our sonship and inheritance by the taint of original sin, and though some lose it after Baptism by subsequent unbelief and sin, neither of these causes are sufficient to remove from God the appellation of Father in a general sense, though certainly these causes remove our worthiness to have Him as our Father.
Here is an excerpt from my communication with a Latin translator I hired to help me understand the sense of this text from the Roman Catechism:
I asked "Is "jure omnium hominum" referring to "ex hoc singulari munere, quo hominem ornavit" or "Pater in divinis scripturis appellatur", or is it possible to read it either the one way or the other? Which way is more tenable?"
The reply I received was "Jure omnium hominum is referred to the gift that God gave equally to all men".
That gift is the image of God.
Pope Eugene IV, Council of Florence: "Let mother Church also rejoice. For she now beholds her sons hitherto in disagreement returned to unity and peace, and she who hitherto wept at their separation now gives thanks to God with inexpressible joy at their truly marvelous harmony. Let all the faithful throughout the world, and those who go by the name of Christian, be glad with mother Catholic Church."
I believe the best example of the theology of Pius IX is in Iam Vos Omnes, in which he calls Protestants and other non-Catholics to conversion. In the letter, which is available in Latin, he uses diplomatic language, and calls them "Christians separated from Us", which as we have seen is valid under the consideration that baptism made them Christian, and then false professions of faith separated them (hence losing any true Christian Faith they may have had - they are now fallen away, or false Christians, Christians in name only). In the letter he very explicitly states that the salvation of individuals and nations depends on their returning to the Church, which once accomplished, they can then call God their Father, and have a chance to be saved. He explicitly states that, even if (etiamsi) they acknowledge (agnoscant; recognize, acknowledge, admit, claim) the same Christ, as (veluti; as if, like, as it were) the Redeemer, nevertheless they by no means profess the true faith of Christ, nor do they follow the communion of the Catholic Church (tamen veram Christi fidem haud profitentur, neque catholicae Ecclesiae communionem sequuntur.). This is a clear statement that they do not profess the true Faith, nor the true Christ as a result.
But Pius IX's theology is perfectly in harmony with that revealed by God Himself, even in Scripture:
Deuteronomy 32:5-6: "They have sinned against him, and are not of his children in their filth: they are a wicked and perverse generation. Is this the return thou makest to the Lord, O foolish and senseless people? Is not he thy father, that hath possessed thee, and made thee, and created thee?"
In the first place, those who have sinned grievously are explicitly told they are not of God's children in their filth, and in the second place, they are reminded of the inheritance that could be theirs - that they were created for - by returning to God.
Luke 15:21: "And the son said to him: Father, I have sinned against heaven, and before thee, I am not now worthy to be called thy son."
Now contrast this with the Heretical Prayers of Antipope Leo XIII, where he says "separated brethren, who are still thy children", and "Mussulmans and other infidels who are, like us, thy children". Big difference. "Like us"!? "In the same manner as us"!? We (true Catholics, that is) are children of Mary spiritually, united in the same fellowship, the one true Faith of Jesus Christ, the true vine. Infidels cannot be called children of Mary in any corporeal sense, let alone in this spiritual sense! Like us, indeed!
In the end, it is Pius IX himself who dogmatically reiterated, ex cathedra, the doctrine that "without faith it is impossible to please God and reach the fellowship of his sons and daughters" - exact quote from the Vatican Council, and his exhortations to Protestants were for their return, even as the parable of Jesus about the "prodigal son", and the dictation of the Holy Ghost concerning the "wicked and perverse generation" of Deuteronomy 32.
And then in his very first encyclical, Leo XIII gave us a sign of the changes to come during his counterfeit pontificate:
Heretic Leo XIII, Inscrutabili Dei Consilio, April 21, 1878 (Italian): "No, non è perfezionamento civile lo sfacciato disprezzo d’ogni legittimo potere; non è libertà quella che attraverso modi disonesti e deplorevoli si fa strada con la sfrenata diffusione degli errori, con lo sfogo di ogni rea cupidigia, con l’impunità dei delitti e delle scelleratezze, con l’oppressione dei migliori cittadini. Essendo tali cose false, inique ed assurde, non possono certamente condurre l’umana famiglia a perfetto stato e a prospera fortuna, perché "il peccato immiserisce i popoli" (Pr 14,34): ne consegue che, avendoli corrotti nella mente e nel cuore, con il loro peso li trascinano a rovina, sconvolgono ogni ordine ben costituito, e così, presto o tardi, conducono a gravissimo rischio la condizione e la tranquillità della pubblica cosa."
The same, translated to English: "No, the shameless contempt of every legitimate power is not a civil perfection; it is not freedom that through dishonest and deplorable ways makes its way with the unbridled diffusion of errors, with the outburst of every cupidity, with the impunity of crimes and wickedness, with the oppression of the best citizens. Being such false, unjust and absurd things, they can not certainly lead the human family to a perfect state and to prosperous fortune, because "sin impoverishes the peoples" (Pr 14,34): it follows that, having corrupted them in the mind and in the heart with their weight they drag them to ruin, they upset every well-constituted order, and so, sooner or later, they lead to very serious risk the condition and the tranquility of the public thing."
It started small, and ambiguously, but it grew from there to be explicit and undeniable. Leo XIII made the ambiguous statement that there is one "human family", and later, by his heretical prayers and teachings, he explicitly places infidels in the family of God, through Mary, and Pius XII even goes so far as to say that she, with regard to the Christ's act of Redemption, filled up what was wanting therein. That is an absolute blasphemous and heretical interpretation of the words of St. Paul, as Christ's act of Redemption was fully self sufficient and of infinite value.
For further discussion and detail on these points, and others, please read also:
Crisis in the Catholic Church: The Leo XIII Connection
Antipope Pius XII: "Infidels are our Brothers in Christ"
Pope Pius IX, Vatican Council, ex cathedra: "without faith it is impossible to please God and reach the fellowship of his sons and daughters, it follows that no one can ever achieve justification without it, neither can anyone attain eternal life unless he or she perseveres in it to the end."