obstinately
In a very stubborn and unreasonable way, refusing to change.
Obstinately means stubbornly refusing to change your mind or behavior, even when you probably should. When someone acts obstinately, they dig in their heels and won't budge, no matter what anyone says or how much sense the other side makes.
Picture a student who obstinately insists their wrong answer is right, even after the teacher shows them the mistake in their work. Or imagine someone who obstinately refuses to wear a coat on a freezing day, shivering but still claiming they're not cold. That's obstinate behavior: sticking to your position beyond the point of reason.
The word carries a negative tone. Being determined or standing firm for something important is admirable, but being obstinate means you've crossed into unreasonable territory. You're being difficult and unreasonable, refusing to listen or adapt even when doing so would clearly help.
When characters in stories act obstinately, they often learn hard lessons. Their stubbornness might get them into trouble that could have been avoided if they'd listened to reason.