The inspiration spoken of by Paul is different from the inspiration that inspires an artist to create a great work of beauty or a scientist to invent a grand new theory. Perhaps it would be easier to adduce other scripture to explain it:
So we have the prophetic message more fully confirmed. You will do well to be attentive to this as to a lamp shining in a dark place, until the day dawns and the morning star rises in your hearts. First of all you must understand this, that no prophecy of scripture is a matter of ones own interpretation, because no prophecy ever came by human will, but men and women moved by the Holy Spirit spoke from God. 2 Peter 1:19 - 21
Traditionally, this has been taken to mean that although the bible had human authors, the content of the scriptures is not merely their ideas, as though they as humans simply came up with some brilliant theological things to say. Rather, they wrote as God moved them. Now, does this mean that God is responsible for every single word? Or only the actual ideas themselves? Or what? What contribution is made by the human authors? Well, there's some debate about that. But however we understand the human contribution, it doesn't amount to simply being one guy's opinion. There was a unified mind behind all the writings that we take to be scripture.
Also helpful in connection with the question of the extent of scripture:
But, in accordance with his promise, we wait for new heavens and a new earth, where righteousness is at home.
Therefore, beloved, while you are waiting for these things, strive to be found by him at peace, without spot or blemish; and regard the patience of our Lord as salvation. So also our beloved brother Paul wrote to you according to the wisdom given to him, speaking of this as he does in all his letters. There are some things in them hard to understand, which the ignorant and unstable twist to their own destruction, as they do the other scriptures. You therefore, beloved, since you are forewarned, beware that you are not carried away with the error of the lawless and lose your own stability. But grow in the grace and knowledge of our Lord and Saviour Jesus Christ. To him be the glory both now and to the day of eternity. Amen. 2 Peter 3.16 - 18
Here the writer of 2 Peter affirms that Paul's letters have the status of scripture.
But in the end, Christians must admit that the bible itself does not specifically state exactly what books are scripture, with a few exceptions. So it was necessary for the church to pronounce on such matters given the rise of heresies and the need to distinguish itself from the Judaism from which it sprung. I believe we can have confidence in that decision because, first of all, the standard for canonicity is very high, and second of all, the decision was made unanimously by a united church. We can therefore presume it was led by God in making its decision.
