Leah's resentment of the Bible is a complicated matter and is based on many factors. Overall, the most powerful cause of her resentment of the Bible is that her father's faith leads him to make decisions that cause major negative impacts in her family members' lives and forces her to recognize the flaws in her father, whom she has previously idolized.
Because Leah is a true "Daddy's girl", and sees him as a heroic figure, the realization that his decisions and views are not those that will best serve to protect his own family, including her, she becomes resentful toward that which causes him to form those decisions and views: the Bible. Leah's father's failure to act as protector of his family after bringing them into a challenging, and often dangerous, environment based on his spiritual calling is the downfall of his family. When Leah recognizes that her father does not have much, if any, desire to minister to his family's needs, she realizes that his faith is what is burdening and harming her family.