My teacher insists that I play a piece of music to the metronome marking. ... I have to practise with the metronome on with that exact tempo marking from now on. No other way. I have to play at that tempo at every lesson.
It was the first time that I played in the lesson and my teacher screamed at me saying "I wouldn't want to be accompanied by you!".
Have you tried talking and persuading your teacher that you feel uncomfortable playing at the suggested speed and that you feel it is more suitable to be played at a slower speed?
I would ask the teacher to lay out for you the problems with making the tempo slighty different from what is marked, what is the worst thing that could happen? If the teacher cannot allow you to make changes to the tempo then I think it's time to change.
A teacher is a source for encouragement, if they beat you down it is very dangerous for your progress and can definately ruin your future progress. This example you gave us highlighted a lack of emotional control while teaching which is a sign of a lesser teacher.