Hinata may have shown off how strong she truly is by pushing herself, but unfortunately, in the eyes of her father, her kind and gentle nature makes her far too weak to be named as the Hyuga Heiress. In "Naruto" Manga Chapter 78, Hiashi deems his elder daughter a failure who can't even measure up to her younger sister Hanabi. In the Naruto episode "The Adored Elder Sister," we get a little more insight about what led Hiashi to believe this as well as see Hinata's kindness work against her. During the episode (via Crunchyroll), the two sisters fight each other in a battle before Hiashi and the Hyuga Clan. Hinata actually reaches a crucial moment where she could have beaten her younger sister in the fight, but out of concern for her, she hesitates to deliver the deciding blow. Instead, Hanabi emerges as the victor, and Hiashi ultimately deems Hinata unfit to lead the clan.
From that point, it's an uphill battle for Hinata as she spends much of the series grappling with her diminished self-confidence. But following her Chunin battle with Neji in the flashback episode "Hanabi's Decision," Hinata reveals to her sister that she, like Naruto, is never giving up on becoming better. Not going back on her word is her Nindo way. This is how Hinata is able to grow throughout the series while still maintaining her kind nature despite no longer being the Hyuga Heiress.
