Question: 2 Timothy:3:16-17, when Paul says "All Scripture is God-breathed," is he referring to his own writings and the remainder of the New Testament? What evidence do we have that these should be considered Scripture as the Old Testament is?
Response: When Paul said all Scripture is "God breathed," the Old Testament was fully compiled, but the New Testament was in the making. The Lord may well have revealed to him the importance of his own epistles.
Second Timothy 3:16 is often rightly cited as evidence for sola scriptura. Immediately preceding 2 Timothy:3:16-17 is verse 15, which states that "...from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus." Paul is speaking of Timothy's familiarity with the Old Testament, as he did not have the New Testament in its entirety.
Nevertheless, Timothy had the two epistles written to him. He may have had copies of other epistles as well. Furthermore, this verse tells us that "from a child" he had known the Holy Scriptures, undoubtedly taught to him by a godly mother. The Apostle Paul is declaring that the scriptures available were sufficient to lead one to a saving knowledge in Jesus Christ and were "profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, throughly furnished unto all good works"(2 Tm 3:16-17).
Further, the Apostle Paul quoted Luke:10:7 as scripture in 1 Timothy:5:18, linking it to Deuteronomy:25:4: "For the scripture saith, Thou shalt not muzzle the ox that treadeth out the corn. And, The labourer is worthy of his reward." Paul places the same emphasis upon the Lord's words in Luke as those in Deuteronomy.
Peter wrote of Paul's epistles in 2 Peter:3:16: "As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction."
Consequently, the New Testament Scriptures themselves witness to the conclusions the apostles had reached under the inspiration of the Holy Spirit.