All Scripture is inspired by God and is useful to teach us what is true and to make us realize what is wrong in our lives. It corrects us when we are wrong and teaches us to do what is right. God uses it to prepare and equip his people to do every good work. ~2 Timothy 3:16-17, New Living Translation
The question I asked them was how good a purpose statement is when it comes from the Book attempting to tell us what it's about. Admittedly, every book does that and usually un-apologetically so. A phone book's purpose is all about giving us information, specifically phone numbers and addresses.
No one argues if the phone book delivers what it says it will deliver, despite the fact that numbers are often wrong. But because the Bible speaks about things miraculous, it is often questioned and maligned. But this never seems to bother the Bible. Or its Author...
And this is yet another thing that differentiates Creator from creation. Whereas we do not like to be questioned and attacks can cause us to waver, God stands strong in purpose and mission. God does not worry about our questions or doubts. Our wants to change Him actually change nothing.
So when God inspired Paul to encourage Tim, He knew what He was doing. Whether God meant for this verse to serve as a purpose statement for the entire Bible can be debated, but God stands behind His Word. Yet another reason that He comes first and we merely follow.