Fear was an emotion after all, and wasn't it in the shinobi rules to rid any emotions? To be more exact, Shinobi rule #25: Do not show emotion under any circumstance.
I bet you're all curious as to what that fear is. Well, it's simple. He was afraid of losing someone important. After all he had been through, it wasn't a big surprise. He had already lost all of his family to his brother who he had once loved. Some might suspect that his fear would be of his brother, but it was quite the opposite. He couldn't wait to see that murderer once again, just to kill him personally for what he had done.
Naruto was afraid of a low stock of ramen – nothing else seemed to bother him more and Sasuke didn't know whether that was a good thing or a bad thing - and Sakura seemed to have a case of autophobia. She had stated that if he had left the village that night, she would feel alone, didn't she? He might be able to share his female teammate's fear at one point in his life, but definitely couldn't relate to his male teammate's phobia. Autophobia : A fear of being alone. Loneliness was something he had grown accustomed to though. He had to. That's why, by leaving, he had been doing a favour for his female teammate.
So how, you ask did he leave the village and betray all those that were important to him help his female teammate? Well, I guess you can say, you have to face your fears sometime. He had learned to face his too, killing two birds with one stone. By abandoning all his loved ones, he had also abandoned his fear.
Because - after all - everyone had their own phobias.