The idea "the the Catholic Church claimed to be spiritual Israel" is a fallacy! That existed when Paul penned Romans 2, 4, 9, and 11.
Augustine taught this long before the Catholic Church. They basically "adopted" Augustine's works, which was one good thing they did, despite their other erroneous teachings.
Obviously you are not aware of Augustine's work "The City of God" or you would not attribute "spiritual Israel" to them. It (spiritual Israel), was believed long before the Catholic Church.
The Israel of God is quite easily understood as Matthew 2:15 makes the point:
15 He remained there until the death of Herod. This was to fulfill what had been spoken by the Lord through the prophet: Out of Egypt I called My Son.
Some of the more prominent early Church fathers believed that the Church was spiritual Israel. These are a few quotes from them:
"But what is meant, says he, in the other passage: "This is God, and there shall none other be accounted of in comparison of Him?" That said he rightly. For in comparison of the Father who shall be accounted of? But he says: "This is our God; there shall none other be accounted of in comparison of Him. He hath found out all the way of knowledge, and hath given it unto Jacob His servant, and to Israel his beloved." He saith well. For who is Jacob His servant, Israel His beloved, but He of whom He crieth, saying, "This is my beloved Son, in whom I am well pleased: hear ye Him?" Having received, then, all knowledge from the Father, the perfect Israel, the true Jacob, afterward did show Himself upon earth, and conversed with men. And who, again, is meant by Israel but a man who sees God? And there is no one who sees God except the Son alone, the perfect man who alone declares the will of the Father. For John also says, "No man hath seen God at any time; the only-begotten Son, which is in the bosom of the Father, He hath declared Him." And again: "He who came down from heaven testifieth what He hath heard and seen." This, then, is He to whom the Father hath given all knowledge, who did show Himself upon earth, and conversed with men." [Roberts & Donaldson, Hippolytus, Against the Heresy of Noetus, "Ante-Nicene Christian Library Vol 09." T & T Clark, 1869, Sect.5, pp.56-57]
"I continued: "Again in Isaiah, if you have ears to hear it, God, speaking of Christ in parable, calls Him Jacob and Israel. He speaks thus: "Jacob is my servant, I will uphold Him; Israel is mine elect, I will put my Spirit upon Him, and He shall bring forth judgment to the Gentiles. He shall not strive, nor cry, neither shall any one hear His voice in the street: a bruised reed He shall not break, and smoking flax He shall not quench; but He shall bring forth judgment to truth: He shall shine, and shall not be broken till He have set judgment on the earth. And in His name shall the Gentiles trust." . . . As therefore from the one man Jacob, who was surnamed Israel, all your nation has been called Jacob and Israel; so we from Christ, who begat us unto God, like Jacob, and Israel, and Judah, and Joseph, and David, are called and are the true sons of God, and keep the commandments of Christ." [Roberts & Donaldson, Justin Martyr, Dialogue with Trypho, "Ante-Nicene Fathers Vol 01: Apostolic Fathers." Charles Scribner's Sons, 1913, CXXIII, p.261]
"For the true spiritual Israel, and descendants of Judah, Jacob, Isaac, and Abraham (who in uncircumcision was approved of and blessed by God on account of his faith, and called the father of many nations), are we who have been led to God through this crucified Christ, as shall be demonstrated while we proceed." [Roberts & Donaldson, Justin Martyr, Dialogue with Trypho, "Ante-Nicene Fathers Vol 01: Apostolic Fathers." Charles Scribner's Sons, 1913, Chap.CXXIII, p.261]
"Then is it Jacob the patriarch in whom the Gentiles and yourselves shall trust? or is it not Christ? As, therefore, Christ is the Israel and the Jacob, even so we, who have been quarried out from the bowels of Christ, are the true Israelitic race." [Roberts & Donaldson, Justin Martyr, Dialogue with Trypho, "Ante-Nicene Fathers Vol 01: Apostolic Fathers." Charles Scribner's Sons, 1913, CXXXV, p.267]
"Thus, then, they who are of faith shall be blessed with faithful Abraham, and these are the children of Abraham. Now God made promise of the earth to Abraham and his seed; yet neither Abraham nor his seed, that is, those who are justified by faith, do now receive any inheritance in it; but they shall receive it at the resurrection of the just. For God is true and faithful; and on this account He said, 'Blessed are the meek, for they shall inherit the earth.'" [Roberts & Donaldson, Irenaeus, Against Heresies, "Ante-Nicene Fathers Vol 01: Apostolic Fathers." Charles Scribner's Sons, 1913, Book V.32.2, p.561-62]
"Thus did [Abraham] await patiently the promise of God, and was unwilling to appear to receive from men, what God had promised to give him, when He said again to him as follows: "I will give this land to thy seed, from the river of Egypt even unto the great river Euphrates." If, then, God promised him the inheritance of the land, yet he did not receive it during all the time of his sojourn there, it must be, that together with his seed, that is, those who fear God and believe in Him, he shall receive it at the resurrection of the just. For his seed is the church, which receives the adoption to God through the Lord, as John the Baptist said: "For God is able from the stones to raise up children to Abraham."" [Roberts & Donaldson, Irenaeus, Against Heresies, "Ante-Nicene Christian Library Vol 09." T & T Clark, 1869, Book V.32.2, p.142]
"And again the same speaks thus: "These things, saith the Lord, I will gather Israel from all nations whither they have been driven, and I shall be sanctified in them in the sight of the sons of the nations: and they shall dwell in their own land, which I gave to my servant Jacob. And they shall dwell in it in peace; and they shall build houses, and plant vineyards, and dwell in hope, when I shall cause judgment to fall among all who have dishonoured them, among those who encircle them round about; and they shall know that I am the Lord their God, and the God of their fathers." Now I have shown a short time ago that the church is the seed of Abraham; and for this reason, that we may know that He who in the New Testament "raises up from the stones children unto Abraham," is He who will gather, according to the Old Testament, those that shall be saved from all the nations, Jeremiah says: "Behold, the days come, saith the Lord, that they shall no more say, The Lord liveth, who led the children of Israel from the north, and from every region whither they had been driven; He will restore them to their own land which He gave to their fathers." [Roberts & Donaldson, Irenaeus, Against Heresies, "Ante-Nicene Christian Library Vol 09." T & T Clark, 1869, Book V.34.1, p.148]
"For we are Israelites, who are convinced not by signs, but by hearing. Wherefore it is said, Rejoice, O barren, that barest not; break forth and cry, thou that didst not travail with child: for more are the children of the desolate than of her who hath an husband. Thou hast lived for the fence of the people, thy children were blessed in the tents of their fathers. And if the same mansions are promised by prophecy to us and to the patriarchs, the God of both the covenants is shown to be one. Accordingly it is added more clearly, Thou hast inherited the covenant of Israel, speaking to those called from among the nations, that were once barren, being formerly destitute of this husband, who is the Word,desolate formerly,of the bridegroom." [Roberts & Donaldson, Clement of Alexandria, Miscellanies, "Ante-Nicene Fathers Vol 02: Fathers of the 2nd Century." Charles Scribner's Sons, 1913, Gal 6:15-16, p.47]
