Odds are this will be closed as a duplicate, since it's a not-uncommon question, but, hopefully, this will let you confirm it :)
I believe you are thinking of Asimov's '"Profession'". Most people are 'tape-educated' via a kind of brain-induction, but our hero is told his brain isn't fit for it, and he's sent to the 'House for the Feeble Minded.'
Spoiler:Eventually (after most of the story) he realizes that it's actually an
Eventually (after most of the story) he realizes that it's actually an Institute of Higher Studies, but that candidates have to find that out on their own and understand his place in their society.
You can read it online, here.