… They break away, then break apart, then outright contradict each other. All the while trying to defend themselves with this Council of Trent stuff… .
And “they" refers to all that is called Christian but not in communion with Rome, but which would include those who are critically contrary to core Prot distinctives which originally defined it. Thus a more valid basic comparison would be between those who at least hold to Scripture as the sufficient supreme infallible authority on faith and morals, in its traditional conservative tradition, versus those who hold to the supremacy of the church, and or any other second class status for Scripture. And yes, the RCC does effectively hold to the latter.
Under the former model there is the lack a centralized authority over all, but have different denominations and churches with their own magisteriums which overall require assent to certain core truths which are commonly held (such as the truths of the apostles creed, plus the supremacy of Scripture, and salvation by grace through
effectual faith, versus earned credits and faith in the church). And which contends those who hold to such are part of the one true church.
They certainly can and do disagree on many things, part of which is due to commitment to doctrine, as well as not simply giving implicit assent to a centralized magisterium and the assured veracity it may claim, (which effects the most comprehensive unity, as cults show), yet as evangelicals they exhibit a remarkable spiritual unity that transcends formal divisions, while they also
testify to greater unity in core Biblical moral views and many core truths than their Catholic counterparts (though both are in decline).
And this common consent to basic core truths is also manifest in a common front against those who deny them (cults), as well as extra-biblical traditions of Catholicism.
In matters of interpretation, they do not claim to be assured infallibility, but hold the Scriptures to be the only assured infallible standard for obedience, and providing, explicitly or by due warrant, the Truth needed for salvation and perfection in faith, and providing for the church and magisterium, as well as for the use of reason, creeds and other helps, but as subject to the test of Scripture. Therefore doctrines must rest upon the weight of scriptural warrant, not the declaration of a mere mortal or office claiming assured infallibility.
These can see Scripture, as progressively written,
abundantly evidencing that it was the transcendent supreme standard for obedience and for testing truth claims, and providing for its establishment as such by supernatural means, based upon its Heavenly qualities, like as true men of God are (though others should confirm such). And thus in principle its completion as an established book of books was also provided for, by making it manifest when there was no more like unto it.
And by this means most of the Divine writings of Scripture were established as being so before the church began. And which itself began in dissent from those who held the historical authority, as the church itself followed an itinerant preacher whom those who sat in the seat of Moses challenged as having no authority. (Mk. 11:28-33) But who established His claims upon Scripture and the manner of Heavenly attestation it affirms.
Under the sola ecclesia model you have different churches with different magisteriums with assured veracity, each claiming to be the one true church, but none of which can actually exercise authority over all others. And which can interpret both Scripture and Tradition differently. Thus Orthodox reject the Roman doctrines of universal papal jurisdiction, papal infallibility, purgatory, and the Immaculate Conception (etc.) as being untraditional. And then there are the sedevacantists and other Catholic schisms.
These require assent to certain core truths, with the Roman model in particular being more precise, requiring assent of faith to infallibly defined truths, though it is a matter of interpretation what these all consist off, while (arguably) allowing some dissent in noninfallible teachings, with these existing in different classes (which are not always clear, nor their meaning).
In addition, as very few Bible verses have been infallibly defined, and the principles of interpretation being imprecise, Catholics have a great deal of liberty to interpret Scripture to support their church.
But which can vary, as while they can lay claim to having an infallible magisterium as supreme authority on doctrine, this is very limited, with most of what Catholics practice and believe coming from the Ordinary magisterium, while they lack an infallible interpreter for their supreme authority.
In teaching, her authority does not rest upon the weight of scriptural substantiation, nor are the reasons or arguments behind an infallible decree necessarily infallible themselves, but while she may invoke Scripture in support, such an interpretation only has weight based upon the premise of her authority and assured formulaic infallibility, wherein she has infallibly defined that she is infallible whenever she speaks in accordance with her infallibly defined scope and subject-based criteria. Thus the claim to consistency with Scripture and history rests upon her own “Divine” consciousness.