This question tests knowing a word for someone who is unmoved by pity and stubborn in will. The term that fits both parts—unmoved by pity and pigheaded stubbornness—is obdurate. Obdurate describes someone who is hard-hearted and inflexibly resistant to persuasion, showing little or no compassion while sticking firmly to their stance. That combination of a hard heart and stubborn stance is precisely what the phrase implies. The other terms don’t capture both ideas. Neurotic centers on emotional instability or excessive anxiety, not a lack of pity or stubbornness. Quixotic means unrealistically idealistic or impractical, not about hardness of heart or stubbornness. Deciduous describes leaves or teeth that shed seasonally, a physical trait rather than a personality characteristic. So obdurate best matches the given description.