intransigent
Completely unwilling to change or compromise, no matter what.
Intransigent means stubbornly refusing to change your position or compromise, even when it might be reasonable or helpful to do so. An intransigent person digs in their heels and won't budge, no matter what arguments or evidence others present.
You might see this in a group project when one student absolutely refuses to consider anyone else's ideas, insisting their way is the only way. Or imagine two friends arguing about which movie to watch: if one is intransigent, they won't even discuss alternatives or find middle ground. They just keep saying “no” to everything that isn't exactly what they want.
The word usually carries a negative feeling. Being firm about your principles can be admirable, but intransigence suggests unreasonable stubbornness that makes cooperation impossible. During the American Civil War, leaders on both sides became increasingly intransigent about their positions, making peaceful solutions harder to find.
Intransigent is stronger than just “stubborn.” A stubborn person might eventually come around or at least listen. Someone intransigent has essentially locked the door to negotiation and thrown away the key. They're immovable, uncompromising, and often frustrating to deal with because progress requires at least some willingness to adapt.