obstinate
Stubborn in a way that refuses to change or listen.
Obstinate means stubbornly refusing to change your mind or course of action, even when it might be wise to do so. An obstinate person digs in their heels and won't budge, no matter what arguments or evidence you present.
Imagine a student who insists their answer is correct even after the teacher explains why it's wrong, or someone who refuses to wear a coat in freezing weather just because they decided they wouldn't. That's obstinacy: a kind of stubbornness that goes beyond confidence into unreasonableness.
The word carries a negative feeling. Being determined or steadfast can be admirable qualities, showing strength and conviction. But when someone is obstinate, they've crossed a line into pigheadedness. They're so locked into their position that they can't learn, adapt, or cooperate. An obstinate mule is the classic image: the animal simply won't move, no matter how much you pull or push.
You might hear someone described as obstinately refusing to apologize, or obstinately clinging to a disproven belief. The word suggests that their stubbornness is getting in the way of progress, understanding, or relationships. Sometimes the hardest thing is knowing when persistence becomes obstinacy.