Sincere
To believe your own lies is delusional. That may not be the term you’re looking for, but it’s an accurate description.
“Confabulating” might come near some cases of what you describe.
Unwavering as in he had an unwavable, unshakeable belief?
TCMF-2L
Conviction. The word you are looking for is conviction.
Self-deception is the only term that sums up OP’s exact question, in my view. the other options identified don’t meet the requirement that the person holds the belief just because they’ve said it/want to, even in the case where conflicting evidence is rationally known to them.
otherwise it might fit a combination of commonly listed Cognitive Bias. It’s a little daunting reading through a list of these cognitive bias, and reflecting on how often oneself falls into these very same traps!! quite sobering.
Doesn’t provide a word for it but here’s Carol Lay’s take on this.
+1
How about self-righteous?
Self-righteousness doesn’t imply that what you are saying is false, just that you think that saying it makes you better than everyone else.
Auto-credulity.