As an aside, the church is never called universal or catholic in Scripture. The designation first appears in the Epistle of Ignatius to the Smyrneans 8:2, among a number of other unbiblical statements: “Wherever the bishop appears, there let the congregation be; just as wherever Jesus Christ is, there is the catholic church. It is not permissible either to baptize or to hold a love feast without the bishop. But whatever he approves is also pleasing to God, in order that everything you do may be trustworthy and valid.” It is quite likely that this affirmation of the existence of a catholic church was a later interpolation into Ignatius’ epistle, if Ignatius actually wrote to the Smyrneans at all. There are three different recensions of Ignatius’ letters, a long, middle, and short version. The long version is generally recognized as a spurious fourth century forgery which projects later hierarchicalism and other developing Roman Catholic heresies into earlier centuries. The short recension only exists in Syriac, and contains only the letters to the Ephesians, Romans, and Polycarp, in a version shorter than either the long or middle recensions. The middle recension, the version quoted above, is found in Greek in only one manuscript, the eleventh century Codex Mediceo-Laurentianus. Scholarship is divided about the genuineness of either the middle or short recensions, with some maintaining that all the letters are extremely heavily interpolated and others arguing that “Ignatius bishop of Antioch did not exist” (pg. 66, “Ignatian Problems,” Journal of Theological Studies, C. P. Hammond Bammel, 33:1 (April 1982); see the article, pgs. 62-97, for a discussion of various theories on the authenticity or forging of the allegedly Ignatian epistles.) Even if one assumes that Ignatius actually wrote something similar to the middle recension, and his writings were then corrupted and falsified into the long and short recensions, there is no reason to conclude that the eleventh century Greek codex of the middle recension referring to a “catholic church” does not itself have numerous dogmatic interpolations designed to support later Roman Catholic dogmas—such as Smyrneans 8:2, the verse in question, and its reference to the catholic church— he catholike ekklesia.
“There are, in all, fifteen Epistles which bear the name of Ignatius. These are the following: One to the Virgin Mary, two to the Apostle John, one to Mary of Cassobelae, one to the Tarsians, one to the Antiochians, one to Hero, a deacon of Antioch, one to the Philippians, one to the Ephesians, one to the Magnesians, one to the Trallians, one to the Romans, one to the Philadelphians, one to the Smyrnaeans, and one to Polycarp. The first three exist only in Latin; all the rest are extant also in Greek. It is now the universal opinion of critics, that the first eight of these professedly Ignatian letters are spurious. They bear in themselves indubitable proofs of being the production of a later age than that in which Ignatius lived. Neither Eusebius nor Jerome makes the least reference to them; and they are now by common consent set aside as forgeries, which were at various dates, and to serve special purposes, put forth under the name of the celebrated Bishop of Antioch . . . [among the other epistles, a spurious long form, a middle recension, and a short recension exist, and] there was . . . a pretty prevalent opinion among scholars, that [no form] could . . . be regarded as absolutely free from interpolations, or as of undoubted authenticity. . . . This expression of uncertainty was repeated in substance by Jortin (1751), Mosheim (1755), Griesbach (1768), Rosenm¸ller (1795), Neander (1826), and many others; some going so far as to deny that we have any authentic remains of Ignatius at all, while others, though admitting the seven [middle recension] letters as being probably his, yet strongly suspected that they were not free from interpolation. . . . [T]he question [was reignited] by the discovery of a Syriac version [the short recension, first published in 1845] of three of these Epistles among the mss. procured from the monastery of St. Mary Deipara, in the desert of Nitria, in Egypt. . . . some accepted the [view that only these three short letters] represented more accurately than any formerly published what Ignatius had actually written . . . [while] others very strenuously opposed [this position in favor of the middle recension]. . . . [T]he Ignatian controversy is not yet settled” (Church Fathers—The Ante-Nicene Fathers, vol. 1, The Apostolic Fathers with Justin Martyr and Irenaeus, “Introductory Note to the Epistle of Ignatius to the Ephesians,” ed. Alexander Roberts & James Donaldson. elec. acc. in Accordance Bible Software, prep. OakTree Software, ver. 1.1). While the reference to a catholic church by Ignatius is dubious, Pope Cornelius, writing against the Anabaptist Novatian, and developing a proto-Roman Catholic principle not found clearly before the third century, affirmed that there “should be but one bishop in a catholic church” (Eusebius, Ecclesiastical History, 6:43:11).
Let it also be briefly mentioned that it is indisputable that the so-called “Apostles’ Creed” was not written by the apostles, and its present form, with its profession of faith in a “catholic church,” is a development of the era after the union of proto-Popery with the Roman state. The “Apostles’ Creed” developed from the Old Roman Creed, which simply affirmed faith in the “holy church.” It was “in the late fourth century that catholic began to appear in [various] Western creeds” (pg. 385, Early Christian Creeds, J. N. D. Kelly. London: Longman, 1972. 3rd ed.), in large part to contrast the Roman church with dissident movements including the “heretical” Anabaptists of the age among the Donatists and Novatians. The earliest physical evidence for the Apostles’ Creed itself is contained in the tract De singulis libris canonicis written by the monk Priminius between A. D. 710-724. Both Pope Leo the Great (d. 461) and Gregory the Great (d. 604) appear to have been ignorant of the Creed, and among scholars “very few will be likely to deny that [the received version of the Apostles’ Creed] is to be sought somewhere north of the Alps at some date in the late sixth or seventh century” (pg. 398, 410, 421, Early Christian Creeds, ibid.).
Nobody who read 1 Corinthians 12:13 in the age when Paul wrote it, or, for that matter, any other verse in the Bible, would come to a belief in a universal church. That view must be read into 1 Corinthians 12:13 in the light of later Roman Catholic and Protestant dogma, but it cannot be exegeted from the text itself.