Why is it relevant to know when the apostle Peter wrote the book I Peter?

'When' the Book of 1 Peter was written is critical in determining who actually authored it..

Critical view Most critical scholars are skeptical that the apostle Simon Peter, the fisherman on the Sea of Galilee, actually wrote the epistle, because of the urbane cultured style of the Greek and the lack of any personal detail suggesting contact with the historical Jesus of Nazareth. The letter contains about thirty-five references to the Hebrew Bible, all of which, however, come from the Septuagint translation, an unlikely source for historical Peter the apostle (albeit appropriate for an international audience). The Septuagint was a Greek translation created at Alexandria for the use of those Jews who could not easily read the Hebrew and Aramaic of the Tanakh. A historical Jew in Galilee would not have heard Scripture in this form. If the epistle is taken to be pseudepigraphal, the date is usually cited as between 70-90 by scholars like Raymond E. Brown and Bart D. Ehrman, while a small number of scholars argue for an even later date.