There is a term I've heard (the closest I remember is "willful incompetence") for someone who is unable to do something because they think they can't and thus refuse to even try.
E.g. The term I'm looking for would describe someone who thinks they are bad at math and so any time they are asked a question they even think is a math question they will only answer "I don't know", even to someone trying to explain that it's not even a math question.
IIRC the term doesn't necessarily imply that the person is in fact capable (despite believing otherwise) of the thing, just that they are so unwilling to try that their actual capability, or lack thereof, is rendered irrelevant.
Edit: the idea I'm trying to remember the name of has some similarity to learned helplessness but is less passive: a person this phrase describes would actively argue against someone trying to convince them they are not helpless.
Edit: the term might be applied to the protagonist in the movie "The king's speech", particularly demonstrated in this bit.