It is hard to know why Nephi2 left. There is no given data on exactly how old he was, but estimates gleaned from the text in other places indicate that he would have been about fifty-four years old. Under the Law of Moses, fifty years old was the mandatory retirement age for a priest. Being a priest involved difficult manual labor. They had to slaughter animals, build fires to make the burnt offerings, and care for the temple fixtures. Thus, the Book of Numbers (8:25) says that at fifty, they had to retire. While we may not think of fifty as particularly old, life expectancy in antiquity was much younger.
There is no information about where Nephi2 went, but he may have been leaving on a mission as he had done before. He had previously gone to the land south to do some missionary work in the sixty-third year of the judges, and returned at the end of the sixty-ninth year, almost seven years later. It is possible that he needed to go on a similar mission and expected to be back. He knew that there had been a five-year prophecy, and that the time was drawing near. However, he did not stay to find out what was going to happen, and he left his young son, Nephi3, and his people with that situation hanging over them.