What is a word for "cannot-be-wrong" attitude?

He is simply being obstinate:

stubbornly refusing to change one’s opinion or chosen course of action, despite attempts to persuade one to do so

... or obdurate:

stubbornly refusing to change one’s opinion or course of action

You can find similar words in a thesaurus.

That person is being "self-righteous" or might have a superiority complex.

Self-righteous: convinced of one's own righteousness especially in contrast with the actions and beliefs of others

I think the word is peremptory, which describes a person's attitude as definitive; leaving no opportunity for denial or refusal.