2 Tim is about preaching and teaching. Let’s go over it.
St. Paul exhorts St. Timothy to give oral testimony
Chapter 1 verse 7
For God hath not given us the spirit of fear; but of power, and of love, and of a sound mind. 8Be not thou therefore ashamed of the testimony of our Lord, nor of me his prisoner: but be thou partaker of the afflictions of the gospel according to the power of God;
St. Paul commands Timothy to teach others to teach.
Chapter 2 verse 2
And the things that thou hast heard of me among many witnesses, the same commit thou to faithful men, who shall be able to teach others also.
Let's skip over chapter 3 for now:
Another exhortation to preach.
Chapter 4: 2
Preach the word; be instant in season, out of season; reprove, rebuke, exhort with all long suffering and doctrine.
The whole book is about preaching and teaching!
Do you really want me to believe, that throughout the epistle of 2 Timothy, St. Paul is telling Tim to preach and teach, but in Chapter 3 verse 15-16 he changes and tells him to pass out Bibles? That seems far fetched to me. But lets study the verse in its immediate context. What is the immediate context of the 2 Tim 3:16? Let's look at some of the verses leading up to it.
It remains, oral teaching. Listen. We'll begin in verse 10:
Chapter 3 verse 10
But thou hast fully known my doctrine, manner of life, purpose, faith, longsuffering, charity, patience,
I have taught you and you have learned.
Skip to verse 14
But continue thou in the things which thou hast learned and hast been assured of, knowing of whom thou hast learned them;
So practice what you have learned considering from whom you have learned them.
verse 15
And 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.
Now, think about this carefully. Does a child have to know how to read in order to know the Scriptures? In my house, my children and I meditated on the Scriptures since before they knew how to read. So I know that the answer is, "No."
Now, let's break down the verse itself
Chapter 3 verse 16
All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
All scripture is given by inspiration of God,
Is that true? Yes. Remember what St. Peter said:
2 Pet 1:20 Knowing this first, that no prophecy of the scripture is of any private interpretation. 21For the prophecy came not in old time by the will of man:
but holy men of God spake as they were moved by the Holy Ghost.
So, all Scripture is inspired. But that doesn't say that Scripture alone is inspired. It says that men were inspired to PREACH. Yes, to PREACH. These men then turned around and wrote down the Scripture.
To say that Scripture is inspired by God is a short hand manner of speaking which means that men who were inspired by God to preach His Word, wrote the Scripture.
and is profitable for doctrine,
Profitable for doctrine. But profitable does not mean necessary.
for reproof, for correction, for instruction in righteousness:
Is it fair to ask who is doing all this reproving, correcting, and instructing in righteousness? Is it not a teacher? If so, does this verse not assume the existence of a Magisterium and thus support the Catholic Doctrine of handing down Tradition by an appointed Teacher, (Magisterium means Teacher).
Bottom line
The entire book of 2nd Timothy is about preaching, teaching and handing on Tradition. 2 Tim 3:16 does not support Sola Scriptura. It supports the Catholic model of handing on the Word of God by Tradition and Scripture in accordance with the consistent Teaching of the Magisterium of the Church.