What iniquity is Nephi talking about? If there is a prophet in history who could be characterized as faultless and faithful, it would be Nephi. He has faithfully returned to Jerusalem twice, traveled in the wilderness, he was the only member of his family who did not murmur when the family was suffering with hunger, he built a ship, and remarkably didn't complain when bound on the ship for three days. What is bothering him?
The record makes it clear that not long after the glue of the family, Lehi, had died, the conflict between Nephi and his older brothers sharpened (v. 13). In the past, it had seemed as if Nephi was not bothered by his brothers' attitude and anger. At this point, the family is in a crisis. Nephi is angry with his brothers for being angry with him. This anger is what he is referring to in these verses, why should I give way to temptations, that the evil one have place in my heart to destroy my peace and afflict my soul? Why am I angry because of mine enemy? Awake, my soul? No longer droop in sin. Rejoice, O my heart, and give place no more for the enemy of my soul, Do not anger again because of mine enemies (v. 27-28).