One of the courses I teach at DTS is NT113, our New Testament Introduction course. Part of the class covers special introduction, which is the discussion of who wrote the books of the New Testament, when and why they were written, and so on. It's sometimes difficult to illustrate why this information is important, except from a general admonition that it helps in understanding a book's content. Thankfully John Dominic Crossan's recent piece in the Huffington Post about the non-Pauline authorship of Pauline books gives me a great example of why this question is important. Crossan is Emeritus Professor of Religious Studies at DePaul University, and is well known for his work on the Jesus Seminar. Biblical exegesis is both analytical and synthetic. It examines the individual pieces, but it also organizes them into a consistent whole. If you are working to understand what an author wrote in one place, it is helpful to compare it to what he wrote elsewhere. Thus as far as biblical exegesis is concerned, it is important to know who wrote which books so you can readily examine the entire complement of an author's texts. This also helps in topical studies and biblical theology, as one seeks to understand how a particular author thinks.
Traditionally scholars regarded all of the books in the New Testament attributed to Paul as actually written by him. However, within the last 300 years or so, scholarship has turned in the opposite direction. If you put all New Testament scholars in a room--liberal and conservative, confessional and not--many would express doubt that Paul wrote all of the books attributed to him, and some would doubt that he even wrote most of them. (This would not be the case at my school or other evangelical seminaries, of course, but it would be true across the board.) Crossan would fit in the group that doubts Pauline authorship of many of the Pauline books.
As you read Crossan's piece, you get a clear picture of where he is going. He states the following about the consensus regarding Pauline authorship:
In other words, we have seven letters certainly from the historical Paul (Romans, 1-2 Corinthians, Galatians, Philippians, 1 Thessalonians, Philemon), three others probably not from him (Ephesians, Colossians, 2 Thessalonians) and a final three certainly not from him (1-2 Timothy, Titus).
One could then argue for a moderating position, as many do, that even though certain books might not be authored by Paul they are certainly Pauline and in accord with his teaching. Crossan does not allow for moderation in this case; instead he argues essentially for rejection.
The problem is that those post-Pauline or Pseudo-Pauline letters are primarily counter-Pauline and anti-Pauline. What happens across those three sets of letters is that the radical Paul of the authentic seven letters (Romans, 1-2 Corinthians, Galatians, Philippians, 1 Thessalonians, Philemon) is slowly but steadily morphed into the conservative Paul of the probably inauthentic threesome (Ephesians Colossians, 2 Thessalonians) and finally into the reactionary Paul of those certainly inauthentic ones (1-2 Timothy, Titus). In other words, the radical Paul is being deradicalized, sanitized and Romanized.
And in Crossan's view this resultant Paul (and the books he authored) should be soundly rejected.
Now it is fair to say that there are other things which contribute to Crossan's historical reconstruction: the assumption that a single author cannot express himself differently throughout his career on a particular topic, the argument that the expression of organization in church structure is contrary to a more spontaneous expression and by necessity later, and so on. But the point I wish to make here is that his conclusions about authorship go hand-in-hand with his exegesis of particular passages. He has concluded that Paul did not write to Timothy or Titus; thus he understands the teaching in those books to be Romanized and late. One would have to understand a different meaning if Paul did in fact write those books, which I and many other evangelical scholars do.
The question of who wrote the biblical books is not an esoteric, academic question. It is a live issue that directly impacts how we understand the text. Time investigating that question is time well spent.