Agreed, but does this verse teach the Scriptures alone?
Verse 10 supplies the context, "Now you have observed my teaching, my conduct, my aim in life, my steadfastness . . . "
St. Pul is writing to St. Timothy, whom we are first introduced to in Acts 16, the son of a Jewish woman who is a believer (what Christians are often referred to in various places in the NT). Of course his dad was a Greek (tree stump worshiper, gentile, pagan). This is a pastoral letter and one of Paul's final epistles. He is nearing the end of his life and reminding Timothy, a bishop in Ephesus, and reminding him of what he had learned and who he had learned it from, St. Paul himself, what he preached, how he lived his life. St. Paul makes no mention to Timothy about what he wrote.
Do reconsider that.
2 Timothy 4:13 The cloke that I left at Troas with Carpus,
when thou comest, bring with thee, and the books, but especially the parchments.
St. Timothy is also reminded of were and how he learned the faith from his childhood from his Jewish mother. What sources did she use to teach him? The Scriptures of Israel, the OT, in particular, the Torah. In 2 Timothy chapter 1 we read a little more about Timothy. In verse 4, the faith first dwelt in his grandmother, then his mother and finally him. Paul is telling Timothy to hold fast to what he has learned from the Scriptures known since childhood. In all of Paul's writings, Scriptures, refer to the OT. It is not until the middle of the third century that the early Christians begin to refer to the NT as Scripture. During the time of Saint Paul and the early Christians there was not a written New Testament. The final book of the New Testament in not written until the end of the first century and it is not for two more centuries that we have some sort of list or collection of the NT. These first lists are the formation of the lectionary. The Liturgy forms the canon of Scripture.
I would say that it is an oversight to limit the availability of scripture to just the New Testament when in the Book of Acts, we see letters/epistles being written.
Acts 15:22 Then pleased it the apostles and elders with the whole church, to send chosen men of their own company to Antioch with Paul and Barnabas; namely, Judas surnamed Barsabas and Silas, chief men among the brethren: 23 And they wrote letters by them after this manner; The apostles and elders and brethren send greeting unto the brethren which are of the Gentiles in Antioch and Syria and Cilicia..... So when they were dismissed, they came to Antioch: and when they had gathered the multitude together, they delivered the
epistle:
1 Corinthians 5:9I wrote unto you in an
epistle not to company with fornicators:
2 Corinthians 7:8For though I made you sorry with a letter, I do not repent, though I did repent: for I perceive that the same
epistle hath made you sorry, though it were but for a season.
That was about not having excommunicated the sinning brother and then when the church did but the brother repented, they let him back in.
Were all churches instructed with access to Paul's epistles? Concerning the collection for the saints, all churches were to be instructed.
1 Corinthians 16:1Now concerning the collection for the saints, as I have given order to the churches of Galatia, even so do ye. 2 Upon the first day of the week let every one of you lay by him in store, as God hath prospered him, that there be no gatherings when I come.
More evidence that the N.T. was to be shared to all churches AND unto all the brethren..
Colossians 4:17And when this
epistle is read among you, cause that it be read also in the church of the Laodiceans; and that ye likewise read the
epistle from Laodicea.
1 Thessalonians 5:7I charge you by the Lord that this
epistle be read unto all the holy brethren.
Even Peter testified that Paul's writings were on par with the rest of scripture as not running against scripture whereas some that err do wrest the scripture to their own destruction;
2 Peter 3:15 And account that the longsuffering of our Lord is salvation; even as our beloved
brother Paul also according to the wisdom given unto him hath written unto you;
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.
Just because they have carbon dated the earliest manuscripts, it does not mean that was when they had started writing & copying scripture. Indeed, the four gospels had to be written down for them to be copied and used repeatedly that there can be no earliest manuscripts during the disciples days. They had books and parchments to copy and share epistles, the four gospels, and even the Old Testament so the churches can have them.
Due to his failing eyesight, Paul had someone write for him as Paul dictated.
Romans 16:22I Tertius, who wrote this
epistle, salute you in the Lord.
So God was able to raise up the N.T. with the O.T. for to be read in all churches to every believer in the very early church days.
Paul even testified indirectly about the apostle John for the Book of Revelations..
2 Corinthians 12:1It is not expedient for me doubtless to glory. I will come to visions and revelations of the Lord. 2 I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth
such an one caught up to the third heaven. 3 And I knew such a man, (whether in the body, or out of the body, I cannot tell: God knoweth
4 How that he was caught up into paradise, and heard unspeakable words, which it is not lawful for a man to utter.
So there is more than enough evidence that the Bible was collected, both N.T. as well as the O.T. by the churches to read to the churches & all the brethren in Timothy's days.