We can banter about, back and forth, all we want - but NONE of these arguments are going to come to a true and final outcome when we operate from wholly variant premises. If we boil it down, we're left with AUTHORITY.
The Catholic position could be summed up to that Latin phrase - which can be translated to "The Church Alone." Catholics believe that Jesus Christ not only promised to build His Church (Matthew 16:18), but actually DID it - starting at John 21:15-17 (just before He ascended into Heaven). THAT Church has existed from THAT DAY forward to the present. Sola ecclesiam does not supplant Scripture - it includes Scripture!
Much of Protestantism clings to this 16th century innovation (never heard of before that time). This is Latin for "Scripture Alone." A fairly accepted definition of sola scriptura is: "Scripture alone is the sole infallible source of instruction for the Church." Some take this to the extreme and proclaim, "If it's not in the Bible, don't believe it." Slightly lesser on the extremist side would be "If it's not in the Bible, you don't have to believe it." A problem here is that Scripture itself NO WHERE teaches sola scriptura! So, if it's not in Scripture, the sola scriptura adherent is either a) bound NOT to believe it or b) OK with rejecting it, but then it is reduce to relative insignificance and certainly not a foundational belief.
Another problem with sola scriptura is that it's never truly "alone." Fundamentally speaking, every Protestant is left to decide for him/herself what Scripture is really saying. This leaves us more with the third position...