All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness.
There are several problems with using this quote as the basis of believing the Bible is the Word of God:
First off, the letter is a complete forgery. There is very little doubt about it. The current consensus of virtually all Biblical scholars is that this letter and the other pastoral epistles where written by some author or authors other than Paul. The language, writing style and vocabulary are irreconcilably different from all the known writings of Paul. There are also references and allusions to documents and events which were written or occurred after Paul’s death. For example, Paul quotes The Gospel of Luke in 1 Timothy. Luke was written about 80 AD at the earliest. Paul died in 67 AD. Documents like the pastoral epistles are called pseudepigraphical. They were quite common in those days.
Secondly, assuming for the sake of argument that this letter was genuine, it is certainly not self-referential. In other words, even if Paul did write it, he was not calling his own letters scripture 1. He was referring specifically to the Old Testament. His own writings were not necessarily the Word of God and could therefore be just a matter of opinion 2. Otherwise, this would be committing a logical fallacy called a “circular argument” or “begging the question”. To say that any statement is the Word of God based on the statement itself would be absurdly illogical.
Third, the word, “inspiration”, is ambiguous at best. If an artist is “inspired” by a muse, does that mean that the muse personally guides every stroke of the brush or pen? Of course not. A clue to “Paul’s” meaning of the word is when he says it is “profitable” (other translations say merely “useful”). If he meant to say that the Bible is truly the very Word of God, then this would be the understatement of the millenia! It is like saying that air is “useful” for breathing. The proper word here would be “necessary” or “essential”. This “Paul” clearly means “inspired” in the more general sense.
Finally, and I can not stress this strongly enough: there is only one Word of God and it is not a book. It is a person whose name is Jesus Christ (John 1:1) . When we elevate an inanimate object, such as a book, to the same level as Jesus Christ we are in danger of committing idolatry.
1 [Here, some people might point out that in his second epistle (2 Peter 3:16), Peter seemed to suggest that Paul’s letters should be considered on par with scripture. The problem here is that the real Peter was illiterate and couldn’t have written the letters attributed to him (Acts 4:13). As an unschooled fisherman, he would not have even spoken the erudite language they were written in. Furthermore, it is well known that Peter and Paul disagreed on many issues. This would certainly not be the case if Peter thought Paul always spoke the Word of the Lord. Peter’s letters were obviously pseudepigraphical as well.]
2[See 1 Corinthians 7:12, 1 Corinthians 7:25, 2 Corinthians 11:17 for a few examples of where Paul admits his words are his own rather than the Lord’s]