As a concerned adult, Yura should have put a stop to the fight before it could begin. But she and--more importantly--THEY were ninjas. The fight hadn't come about because of a quarrel. It was meant to demonstrate their skill to each other--even if they would probably take a little too much relish in doing so. So in her mind it wasn't a bad thing. Ninja will be ninja. 

She followed them at a distance and then sat on her back porch to watch. This should be interesting. 

Naruto was ablaze with energy. He'd eaten his first good meal in who knew how long and someone had been nice to him and now he got to fight Sasuke! There was a little irritation at being told Sasuke would defeat him--but Naruto knew that was just smack talk.

"You don't stand a chance, chicken head! I'm gonna plant that smirk of yours in the dirt!" 

Once Sasuke was ready, Naruto initiated the fight. 

By flinging himself wildly forward. There wasn't a lot of finesse in him. But he roared enthusiastically as he aimed for Sasuke's head.