Invincible ignorance fallacy.

The invincible ignorance fallacy (a.k.a. argument by pigheadedness): when a person simply rejects any evidence presented and unquestioningly sticks to their prior belief.

We all have trouble changing beliefs. We have emotional attachments to many beliefs, and some are important parts of our identity.

So we are probably all prone to the invincible ignorance* fallacy in some domains.

I think it is misnamed. You could have a correct belief and still engage in this fallacy, so fearful of challenging the belief that you will not consider plausible evidence against it.