As a result of her kind, caring, and softhearted attitude, it's easy to confuse Hinata Hyūga as an apathetic fighter. Despite her shyness, Hinata wanted to prove her worth to the world, especially to her family. It's why, according to the character databooks, Hinata wished for a rematch against her cousin, Neji Hyūga. As "Naruto" fans know, Hinata was matched against Neji in the Chūnin Exams arc and lost. Even though Naruto defeated Neji in her honor, Hinata wanted to fight Neji one more time, presumably to show her growth as a fighter. Unfortunately, the rematch can never happen, as Neji sacrificed his life for Naruto and Hinata in Episode 364 of "Naruto: Shippūden." 

Hinata's desire to fight her father, Hiashi Hyūga, also presumably comes from the same motivation to fight Neji — Hiashi originally gave up on Hinata becoming the successor of the Hyūga Clan when she was a child, choosing to focus on her sister, Hanabi Hyūga, instead. Today, we know Hiashi's relationship with Hinata has changed for the better. This is thanks to Naruto getting through to Neji before his death by changing his limited outlook on life, which led Hiashi to re-evaluate his own philosophy and relationships with others.