DEPENDS on which CUNTRY you belong to!
The REAL WORLD is very DIVERSIFY, it's created by the INFLUENCE OF NATURE on the people dwelling in different parts of the world.
For example, DESERT people tend to live "simpler lifes", and ABSOLUTE obeisance is cherished <so nobody will correct a teacher or even be able to detect errors by the teachers>
On the other hand in HIGHLY diversify enviroment with PLEASANT WEATHER like Mediterranean to temperate climate region - FAUNA is plenty & produce is VAST and plentiful, easy to access = TEACHERS will prefer some DEBATE to "protect & enhance" his skills.
A teacher being "TOLD" he's in error by a student - IS MOST WELCOMED - as the CHALLENGE creates THE INQUIRY. In most cases, YOUNG CHILDREN are unable to do so, requiring "spoon feeding" EXCEPT for the more TALENTED ---- who thinks he/she has spotted a "teacher's error".
People's talent is HIGHLY UNEVEN, even TEACHERS are of UNEVEN qualities......
This morning, our teacher did not recognize a word and pronounced incorrectly. Then one student helped him correct it, but he just prentended not sounded. So it's very common in college when a teacher makes a mistake, he may just neglecet it.