1 Ne 6:1 the genealogy of my fathers.... is given in the record which has been kept by my father
This verse makes it clear that Nephi is still abridging the record of his father. The most important part of one's genealogy in Lehi's day was to show descent through Israel. The Jews did have a habit of declaring long genealogies. Paul warned about this when he wrote to Titus, "But avoid foolish questions, and genealogies, and contentions, and strivings about the law; for they are unprofitable and vain (Titus 3:9) Nephi declares his father's lineage through Joseph then kindly spares us the details of who begat whom from Joseph to Lehi.
1 Nephi 6:5 the things which are pleasing unto the world I do not write
Not everyone responds to the Book of Mormon the same way. Some intellectuals find the book useless. Even some members never seem to get the Spirit of the book. But, such a response says more about the individual than it does about the book. As Paul taught, 'the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned' (1 Cor 2:14).
"[Nephi] tells us he is going to give us an abbreviated account. 'Wherefore, the things which are pleasing unto the world I do not write, but the things which are pleasing unto God and unto those who are not of the world' (1 Nephi 6:5). That's important. The Book of Mormon is not to be peddled for entertainment or TV fare. It's not meant to be diverting. Mark Twain said, 'It's simply chloroform in print.' Most people can't even get through it; they think it's the dullest book in the world. We know it's anything but that, but it isn't written as a best seller. It isn't written for the sake of the story or the thrills...When you pick up the Book of Mormon, you [have to] shift your mind into another gear..." (Teachings of the Book of Mormon--Semester 1: Transcripts of Lectures Presented to an Honors Book of Mormon Class at Brigham Young University, 1988-1990, p. 171.)
Neal A. Maxwell
"Naturally, some would like to have even more contextual material about the life, times, and culture of the peoples in the Book of Mormon. In fact, though, there is much more already given in the book than most of us have been able to assimilate and appreciate thus far. Nevertheless, such supportive but ancillary data are not the purpose for which the book has been brought forward. This reality is stated very early in the book itself: 'Wherefore, the things which are pleasing unto the world I do not write, but the things which are pleasing unto God and unto those who are not of the world' (1 Nephi 6:5).
"No wonder these scriptures fail to please or to impress the world. There are those who prefer details on ancient agriculture to the 'bread of life,' who prefer information on the rising of dynasties to insights on the rising of Jesus from the tomb. Perhaps this is so because the former type of data is very interesting without being very demanding. The second type demands both faith and, thereafter, a certain behavior." (But for a Small Moment, p. 38)
1 Ne 6:4 that I may persuade men to come unto the God of Abraham.
Nephi declares his intent to persuade men to come unto the God of Abraham. His record begins with this invitation for the readers to come to Christ. It sounds like an invitation without obligation. However, by the time Nephi finishes his record of the things of God, the Spirit prompts him to hold the reader responsible for how they receive his writings, 'And if ye shall believe in Christ ye will believe in these words, for they are the words of Christ, and he hath given them unto me; and they teach all men that they should do good. And if they are not the words of Christ, judge ye--for Christ will show unto you, with power and great glory, that they are his words, at the last day; and you and I shall stand face to face before his bar; and ye shall know that I have been commanded of him to write these things, notwithstanding my weakness....for these words shall condemn you at the last day.' (2 Ne 33:10-11,14)