Shakugan No Shana last season

Can anyone explain to me what was Yuuji fighting for, especially at the end where he already accomplished his objective,but still fought Shana

This is just speculation but I think that it was just to express how much he wanted his ideals to be acknowledged. They said that flame hazes were bound to their fate but Yuuji wanted otherwise, to relinquish destiny itself, even after the grand scheme was finished and the snake of the festival gone, he wanted to show her that he'd rather die by battle rather than give into fate.