Social: There are two pieces of information in this verse. The first is that this people appointed a king. This tells us that they were in conscious rebellion against their over king, and were creating an alternate society. The fact that they created a king also suggests that this group contained a kin group that had some claim to the throne. It is possible that their defection was a result of their inability to further the political interests of the kin group within the established structure. Since the current king in Nephi was an apostate Nephite who had only recently been seated after a conquest, it is possible that these rebellious peoples were related to the political establishment from the prior ruler, but were not among those who converted to the Nephite religion. They would therefore have had a legitimate claim to the throne which was removed from them by the external conquest. Their desires to move into that position could explain their actions.
This leaves us with the second piece of information in the verse, which discusses their motivation for the separation from the king in Nephi. We should remember that this is Mormon’s version of their reasons, and there is no way that he could have had access to records that would accurately describe the motivation of this separatist group. The gross outlines of the actions could easily have been reported and made their way into Nephite annals, but the motivations would not have been faithfully recorded. Thus this is Mormon’s interpretation of the reason, and one that implicitly exalts the Nephites. That subtle exaltation of the Nephite military prowess does make this an appealing reason for Mormon, but it is probably his analysis rather than an accurate record of the reasons for this split.