2 Timothy 3:16
“All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness,”

This verse is often used by some to try to prove that the Bible is the God given word and it is therefore infallible.
There is much debate as to whether Paul wrote this letter. Paul was said to be executed in 62AD and the letter was written in 67AD. This has led to many arguments as to when Paul was killed and some have tried to extend Paul’s life to accommodate this issue. There is also much debate as to the style of the letter being different from other written material of Paul’s. This has led many theologians to call - 2 Timothy a “Pastoral letter” (i.e. written by some unknown person in early Christianity, but not Paul).
‘1 Timothy’ and ‘Titus’ are also considered Pastoral letters. Some early Christians (Syria Orthodox for example) refused to accept the 2 Timothy as genuine and thought it a forgery.

So let us now consider the verse in relation to the Bible. The Old Testament was agreed to be scripture by the Jews in 90AD at the Council of Jamnia and the New Testament was declared scripture by the Eight Council (at Carthage) in 397AD. Therefore, 2 Timothy, being written in 67AD preceded any recognition of the Bible (OT & NT) as scripture. This is not to say that many writings were not treated as scripture even if they were not fully recognized as such.
The verse is believed to refer to the importance of scriptural writings in educating of new Christians. It is not meant to mean that the Bible or Scripture is somehow infallible and God spoken (IMO).
The term used does not even mean “scriptural writings” (Grammata) but uses the word “Grapha” (meaning the process of describing and the grasping of moral or metaphysical truths).
In other words it can be understood that all seeking of God and finding truths is God breathed. The Bible can be used to do this and indeed is important to all Christians, but in no way is the verse saying that the Bible is an exclusive way to do this.
In this understanding, the verse makes sense to me, given some of the terrible things spoken of in some passages of the Bible. The Bible does have lessons that I feel are important but it also shows some of the very human mistakes that we can make in our understanding too.