Surely the window shades, not the windows !
It's common on many carriers for the carrier's safety & security policy to require shades up for all seats for landing & takeoff. The reasoning being that it permits a double-check that in an emergency the aircraft is not upside down or otherwise facing a fire or other dangerous situation.
If the FA told you this during level flight, she is most likely poorly trained. If it's bothersome, send a note to AA asking that the crew be retrained.