My Problems with Sola Scriptura

So, chatting about Our Lady (see here) led us onto Sola Scriptura.

I have several problems with Sola Scriptura:

1 Sola Scriptura isn't in Scripture. That seems fairly fundamental. I asked my interlocutor about this, and he replied: Scripture is God-breathed (2 Tim 3:16). B/c Scripture is the only God-breathed revelation possessed by the church, it forms the only infallible rule of faith for the church. But clearly what the quotation actually says is Scripture is God-breathed.  The rest, B/c Scripture is the only God-breathed revelation possessed by the church, it forms the only infallible rule of faith for the church' is an interpretation. But on whose authority is that interpretation? It is not scriptural.

2 Sola Scriptura fails because the Scriptures themselves do not contain a definite list of the Scriptural books. We know what those books are on the authority of the Church and Tradition. How else do we know that the Gospel of Thomas or the Shepherd of Hermas are not scriptural?

3 Sola Scriptura is against Scripture. For Scripture teaches that the Church is the pillar and foundation of the truth; in Scripture we read of Christ conferring the office of teaching on Peter, in first place, and the apostles. We read that he who hears the apostles, hears Christ. We read of the authority of the first Council of the Church. We read that we should obey whatever the Apostles teach by word or in writing. We read of the Apostolic succession, with the replacement of Judas. And of course the early converts did not have the New Testament: it had not all been written - so did they have no 'infallible rule of faith?' And on and on...

4 Sola Scriptura is a modern invention: the idea was formulated by Luther to justify his rejection of the authority to which he had sworn obedience.

5 Sola Scriptura has never been held by the vast majority of Christians: the Orthodox and the Catholics.

5 Sola Scriptura does not work. Those who adhere to it cannot agree what Scripture teaches. Since Luther's rebellion, protestantism had fragmented and fragmented further.

6 Sola Scriptura is the subject of regular debate between Protestant and Catholic apologists: how could this be, if it were as self-evidently true as Luther (who could not even agree with Zwingli) proclaimed? The fact that it can be debated at length, with both sides quoting Scripture at length, and neither side convincing the other, demonstrates that Sola Scriptura cannot be the sole infallible rule of faith.

None of which, of course, in any way diminishes the truth of Scripture as the Word of God. But it is the book of the Church, and it is the Church that is the guarantor of its inerrancy, and the guardian of its correct interpretation.