Big Picture or Details?
I agree that the result is that the contents of Scripture are inspired but nevertheless it would bring a certain nuance out to discover whether or not Paul was emphasizing the details (every part) or summarizing about the collective whole. There are certain pastoral implications of preferring the emphatic attention to segments or detail, in contrast to what I would consider the more common interpretation at this point of the passage. For example, justifying the importance of fine-tooth-combing the Word for minutiae and seeking to bring application to even obscurities therein, as distinct from the typical over-simplification/big-picturizing which our culture is more and more hungry for. In my opinion we often tend to be intellectually lazy anymore and therefor we need all the exhortation we can get to get back to "every part" of the text, not just our favorite topics.
2 Timothy 3:161, 2 Timothy, Titus
3:16 Paul’s observation about the effect of Scripture in Timothy’s life led him to make an assertion about the inspiration and usefulness of Scripture. We must not view Paul as attempting to inform Timothy of the inspiration of Scripture. Timothy had heard this truth since childhood. Paul was reminding Timothy that Scripture was profitable and “that the basis of its profitableness lies in its inspired character.”47 For additional discussion on the subject of the inspiration of Scripture, see Excursus