Nephi makes no explicit mention of the reasons why he was unable to take his father's dream on face value, why he found it necessary to experience the dream's content for himself. He simply mentions that he was desirous to see and know those things. Remember that this is a new wrinkle in Nephi's relationship with his father as a prophet. While Nephi has recorded the fact of his father's visions before, he has never indicated that he required a personal revelation concerning them until this point. Why now?
As indicated above, I suggest that one reason for Nephi's desire to experience the same information stemmed from the disconnection of the elements of his father's dream and Nephi's cultural expectation of those symbols. The second reason is clear in this verse, Nephi wants to know more about the Messiah.
Why was the vision of the Tree of Life and the discussion of the mission of the Messiah connected in Lehi's discourse and subsequently in Nephi's experience? Precisely because the nature of the Tree of Life symbolism branched into a connection with the King, in this case, the Messiah as the coming ruler.