Sola Scriptura is not scripture alone any more than Sola Ecclessia is church alone!!!
Sola Scriptura is that scripture is the ultimate authority!
The problem here is that Catholics would like to argue that the three authorities of tradition, church and scripture are equal but that is simple and quite obviously not true. The church is the ultimate authority over scripture and tradition which is clearly NEVER taught by Christ or believed by the early church. If there's any doubt about this, we have to ask...
i) Who decides what scripture really means? THE CHURCH
ii) Who decides which traditions are sacred and which are not? THE CHURCH
iii) Who is the ultimate authority? THE CHURCH.
Protestants do have 1,000 of denominations but I'm going to go further and say MILLIONS of different beliefs because within those denominations we have people believing and disbelieving many different things. This is because we all err to Customised Christianity... or Christianity we think is true irrespective of what our denomination or others believe. The problem is that Catholics WANT to believe they are united in their faith and it's a complete lie... and it's troubling they cannot see and parade their assumed unity as if it's a demonstration of their pious righteousness (much like the clergy of the first century). The thing is that Catholics, maybe on a subconscious level, know and can see their unity is not true because within every church there are Catholics who don't believe everything the way the church teaches it.... but let's go further and demonstrate this disunity more widely so as to demonstrate the fallacy of it....
To be a Catholic one MUST believe in the divine beliefs called dogma. These are the non-negotiables of Catholicism. If you don't believe in any of these then officially you're not a Catholic. Yet, TWO THIRDS of American Catholics do not believe in the dogma of transubstantion. That's two thirds who Catholics in the US who are not actually Catholic!!
Just one-third of U.S. Catholics agree with their church that Eucharist is body, blood of Christ .
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So much for Protestants having unique interpreations!