An unwillingness to give up our beliefs even when the evidence proves us wrong is called

Belief perseverance.

Explanation:

As the exercise briefly states, the unwillingness to give up our beliefs even when the evidence proves us wrong is called belief perseverance. This phenomenon occurs when an individual maintains a belief even though it was refuted by new information. This is also known as conceptual conservatism. All in all, belief perseverance could be defined as stubbornness in changin one's mind when faced with evidence that something we believe in is not true or right.