Not an assumption at all…
“… upon this rock I will build my church…”
I = Christ. He did it. Any other group, regardless of their good intentions, was started by a man… or woman. Thus not the Truth.
My = His possession. Since Truth is unchangeable, any other group which adds, detracts, or changes that which was taught from the beginning… is not the Truth
Church = singular form. Christ uses the word for the first time in the New Testament. No longer is the word temple held in the highest esteem. Only the “group” intended to be of one Lord, one Faith, one Baptism can fully be part of the Church. Thus, all the denominiations that followed are not the Church.
Agreed that the Body of Christ includes all who have Trinitarian Baptism… but rejection of the other principles of Christ’s Church leaves one in the family, perhaps, but living in the back yard outside the house. - The Catholic Church.
The most evident of this is the Orthodox with their rejection of the prime among equals… the Pope.
The next most evident would be the Lutherans, Calvins etc who chose to live outside during the Reformation.
The others, like the Baptists, Pentacostals, Methodists etc are simply more of the many examples of man’s insubordination.
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