1 Nephi 6
I have often wondered about the authenticity of the Book of Mormon. Is it real or is it a made up book? I can see how many people would not believe the story of Joseph Smith, and how many people also might look for more, perhaps in the form of archeological evidence of the Book of Mormon in Central or South America. Nephi does not give his ancestry at this time because it is written in the Book of Lehi (which was lost with the 116 pages by Martin Harris; see D&C 3), but in his defense he reveals a powerful phrase that governs all of our choices: "for it sufficeth me".
I am satisfied with Nephi's explanation of why he didn't include the genealogy of his Father. His genealogy is really not important to me or any of the writings of the Book of Mormon. The Book of Mormon was written by ancient prophets to "persuade men to come unto the God of Abraham, and the God of Isaac, and the God of Jacob, and be saved". It is a book for the spirituality of man and not an archeological record.
One thing my parents taught me about the Book of Mormon is that all the material proof in the world ("the things which are pleasing unto the world") will not make a difference in how you live your life. Spiritual impressions ("the things which are pleasing unto God") are the substance of a spiritual life. I am satisfied with the spiritual manifestations which I have received of the existence of God, of the truthfulness of the Book of Mormon, and of the authenticity of the Book of Mormon.
I want to pass this bit of wisdom to my children as my parents have passed it to me. The Book of Mormon (and any spiritual document) is for our spiritual progression, and does not need to be proven from every angle to be effective in its purpose. Time spent trying to prove this or that may be fine, but time is better spent finding out how this book can help you spiritually progress.