I'm looking for a short story written pre-1975. It has a future world where children are educated to enter a specific guild. The hero is at the top of his class, but does not get selected for his guild. Shunned by family, he is sent away, where he discovers the real reason for his failure: he is too important as a thinker.
This is almost certainly Asimov's "Profession":
George Platen is determined to be a Computer Programmer, a profession in demand, and he hopes to qualify for "export" to a top-flight Outworld. On Reading Day, however, concerns are raised about George's ability to be Educated. On George's Education Day, he is told that his brain is unfit for any form of Education. He is drugged and sent to a House for the Feeble Minded.
"House" and "Simple mind" are not in the title, but they are referred to almost verbatim - "House for the Feeble Minded".
And there, indeed, George discovers that he's wanted as a thinker:
George is returned to the House and discovers the reality: the House is an Institute of Higher Studies. Those people who have the urge and persistence to create, even though they have been told otherwise about their abilities, are sent there to support the advancement of science and civilization.