No text speaks for biblical canons as a whole
Biblical canons (yes, there are more than one; see here) were chosen by a select group of individuals hundreds of years after the individual pieces were written. Consequently, no text in the scriptures can speak for them as a whole. Yet some people still act as if certain passages do.
For example, some people refer to passages that mention the Law (e.g. Matthew 5:18) as evidence for inspiration. The Law, however, is only a part of the scriptures, and it is different in nature since it was (at least partially) written not by the hands of men but by the finger of God (Exodus 31:18).
Evidence for a part is not evidence for the whole. For example, say archeological evidence confirms that a prophecy correctly foretelling a future event was recorded prior to the event. That is evidence for the inspiration of that part of the prophecy that spoke of that event, but it is not evidence for the scriptures as a whole, not even for the whole prophecy (because it’s possible that the writer was correct in the archeologically confirmed part but wrong in other parts).
Inspiration is practically irrelevant
Even if bibles are inspired, I can’t see how that matters at all. Suppose the original writings were inspired in the modern sense. This is no way invalidates the fact that the processes of transcription, translation, interpretation, and application through which they did and do go through are all fallible. Thus the bibles we now have cannot be used in any “absolute” way as a basis for truth. So what purpose is served in declaring bibles to be inspired?
To me it seems to be a way to secure religious power in the hands of those with knowledge (regardless of whether this is done unintentionally or not). Those who know more, and specifically those who have received religious training, have a corner on truth. Intentionally or not, history and the current state of the “christian” world demonstrates that the scriptures have been and are being consistently used in this way.
How the NT authors use the OT
The ways in which NT authors cite the OT makes it seem that they did not believe in inspiration in the modern sense. I previously wrote about this here.
Objection: But I encounter God through reading bibles
Me too. But that doesn’t necessarily mean it is inspired; it only means (at least) that God speaks to us through it. And truthfully, God can speak to us through anything. If you spend a ton of time reading bibles, then of course sooner or later you will encounter God through it. But you can encounter God playing sports or watching movies too. I’m not saying those are of equal value with bibles. I’m only pointing out that the fact that we encounter God through reading bibles by no means proves it is inspired.