Ignatius, a so-called "church father" who lived roughly c. 50-110AD, is the father of the universal church theory, or what he called "Catholic Church" (Catholic means Universal). Later this would form a cardinal doctrine of the Roman Catholic Church.
But who could possibly understand what a “universal assembly” is or to be assembled together invisibly?
The word “church” is translated from “ecclesia.” In Scripture it is only ever referred to as a local assembly, even during OT times, one that is geographically related rather than to a body of believers without respect to location, something I will prove below. The OT indicates repeatedly that it meant the congregation of the Israelites, especially when gathered for religious purposes (De 4:10; 9:10; 31:30; Jud 20:2; 1 Sam 17:47; 1 Ki 8:14). In the NT, Stephen’s sermon is the only time the word is applied to the Israelites while gathered together in the wilderness (Ac 7:38), but never used towards them upon entering the promised land separated geographically into the different tribes.
The word “church” means an assembly, a congregation, one gathered together, and all appearances of the word in the NT have that meaning. Even in the epistles referred to as the “general epistles,” historically named as the “universal epistles” (terms applied to James, 1 and 2 Peter, 1, 2 and 3 John, and Jude, because they were not written to any specific local church) the mentions of this word are obvious local assemblies.
Did the sick man call, as commanded, the elders of the “universal church” or his local church (Jam 5:14)? The respect of persons warned of by James was occurring in “your assembly,” also obviously very local (Jam 2:2).
Third John uses “church” three times (vv 6, 9-10), but is written to “Gaius” (v 1) who is obviously one person in one location at once. That is the same “Gaius” that Paul wrote about in Rom 16:23, where “the whole church” is again clearly a local assembly.
Peter speaks of the “church at Babylon” (1 Pet 5:13) where the letter was sent from, obviously meaning a single assembly in one location. He also uses the analogy of a house built up of lively stones (1 Pet 2:5-7), which obviously means a local assembly as it presents “a spiritual house” (singular) which is made up of “lively stones,” identifying members of a congregation make up the local church. Notice that Peter is writing “to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia” (1 Pet 1:1), expressing that each local church receiving his letter in these regions would understand themselves as “a spiritual house” (singular) in and of themselves; not accumulated as one stone structured together with another stone found in another region many miles away. Furthermore, “the strangers” are not Jews of the diaspora among Gentile nations as commonly claimed, since 1 Pet 2:10 says of these “lively stones, a spiritual house” (v. 5), that they “in time past were not a people” clearly referring to the various groups of Gentiles gathering together in local assemblies.
So one would expect to find this new meaning of “universal church” in these “universal epistles” but just the opposite is in fact the case. Many other passages in Scripture are simply obvious that church is local only: e.g. Rom 16:1, 5, 23; 1 Cor 14:23; Col 4:15-16; 1 Th 1:1; 2 Th 2:1; 2 Tim 4:22; Ti 3:15; Ph 1:2; Rev 2:1, 8, 12, 18; 3:1, 7, 14; etc. The evidence for this is overwhelming.
The first epistle to the Corinthians, which is commonly used to support the “universal church” error, defines church as “the whole church be come together into one place” (1 Cor 14:23), which is clearly an assembling together of people in one locality.
This is how we should understand all of Paul’s usage of the word. If the word “church” (singular) could be or was being understood in a universal sense during the first century in the NT, then why do we find the word used in any plural form, as it is in 35 places? Using a singular noun (“church”) doesn't mean it is "universal," like any other singular noun. When I refer to my phone as "the phone," I am not referring to every single phone in the world, my phone isn't universal, but to one particular one.
The universal church doctrine is actually established in modern Bible perversions based upon the Critical Text (which is the product of later corrupted manuscripts which misapplied the term to a universal sense), further proof why such versions make a big difference on how people understand theology and doctrine.
Does the title “body of Christ” imply a universal church? How many people have ever seen a living body with its members, meaning body parts, scattered over many thousands of miles in separate locations? Paul’s purpose of the analogy of the “body” is to present a local church, which was the common use of the analogy in the first century. In 1 Cor 12:13 where the presupposition is commonly read into the text, the context (vv. 14-30) explains it plainly as a local body. Speaking of what God is doing at Corinth and other local assemblies, v. 24 says “God hath tempered the body together,” tempered meaning composed, united together, speaking of unity in the local assembly, the only unity possible.
Previously Paul had reproved the “church of God which is at Corinth” (1 Cor 1:2), a local assembly, to be united because of the divisions and factions that had developed (1 Cor 1:10; 3:3; 11:18-19). 1 Cor 12:25 declares “there should be no schism [division] in the body; but that the members should have the same care one for another.” How in the world (pun intended) would that be possible outside of a local assembly? Or what about 1 Cor 12:26, “whether one member suffer, all the members suffer with it; or one member be honoured, all the members rejoice with it.” When someone suffers or is honoured in a church the other side of the world, you wouldn’t even know about it!!
The offices and positions (1 Cor 12:28) and doctrines taught (Eph 4:11-16) in the NT Church are only regulated from a local position. One has no say what happens in another church, although one can warn about them (Ju 1:3; Rom 16:17-18) or encourage them. That proves the point as well. The “ye are the body of Christ, and members in particular” (1 Cor 12:27) is referring only to a local autonomous assembly, specifically Corinth here. One body of Christ, with many members. Obviously, a “body” can only function when all its part, or members are in one locality working in accord with one another and that is precisely what a NT church is, an assembly of immersed born again believers organized and united to carry out the Lord’s work. One of the reasons why there is so much disunity in the churches today is because of this "universal church" doctrine (see here).
“Universal church” doctrine is not taught in the Bible. There isn't such a thing — church isn't universal. The universal church as a teaching or belief eisegetes scripture (which is unscriptural interpretation of reading presuppositions into Scripture), distorting the plain meaning of the text and is dangerous. Its what we mostly see with evangelicals today. Red flags are lingual such as “the church of Canada” or “the body of Christ” or just "the church" and the person is not referring to one local church with an actual visible membership but to believers everywhere. You cannot defend it from the Bible. And there is a lot of disobedience that comes because of this doctrine.
None of the passages frequently used, such as Matt 16:18; Eph 1:22-23; 5:30; Col 1:16-18; 1 Cor. 12:12-27; or Rom 8:16 refer to a universal church. When someone comes to the word "church" in scripture, he should read it as a visible, physical assembly. You can't find a spiritualization of it, a universalization of it, anywhere in the Bible, so the burden is on that persuasion. You definitely have to read in the catholic (i.e. universal) idea in order to get it out.
So how is it read in? By spiritualizing scripture or interpreting out of context.