Big misconception around here. They mistake Naruto's destiny for his prophecy. Naruto can change his destiny anytime. His prophecy could be wrong.
Lets start with Destiny:
Maybe you can change it, maybe you can't. I don't know. What I do know is people take their conversation the wrong way. Their argument was about changing destiny, not destiny itself. Neji was basically telling Naruto if you're a loser, then you're a loser. You can't change that. Naruto said you can change it. He also stated Neji didn't believe what he saying about destiny.
The Branch family is destined to protect the Main Family. Neji tried to hurt Hinata because he(himself) didn't believe destiny could not be change. Neji was trying to change his destiny.
Their argument was about changing destiny.
What was Neji's proof destiny could be changed? A loser like Naruto beating a gifted Ninja like him.
Prophecy is nothing, but a prediction. Prophecy stated it was Nagato, then it was Minato. At the end of the day it's Shonen manga and Naruto is the main character. He will defeat the bad guys without question.