Ultimately it boils down to faith in human tradition and faith in the book itself.
If you examine the criteria used for determining the inspiration of bible books you would notice that they're all fallacious and ultimately boil back down to 2 main arguments:
1. "We know bible book A is inspired because the earliest christian writers or earliest Jewish writers considered it to be inspired as evidenced by such and such early writing where the book is mentioned as being inspired." - Appeal to ancient wisdom.
2. "We know bible B is inspired because bible book A quotes or mentions bible book B." - Appeal to circular logic.
The point about the different books being in harmony despite being penned by different people living in the different times, is total rubbish that is easily debunked with a little common sense. Because the books were written years apart, later bible writers had opportunity to read the books of earlier writers. Thus having their thinking shaped by what they read in the earlier books, it is only logical that later writers went on to write books that harmonize somewhat with what was written before.
For the internal harmony argument to have any weight, all the books would have had to be written at the same time by writers living in different locations and unaware of what each was writing. Had that been the case, then the internal harmony argument would have some weight. But as it is with the books written years apart, it is a rather foolish one.