Note that many things are forbidden because of Morris Ayin. Thus, we see that he is regarded as a min (kind) of heretic who is attempting to get (other) people to think that good people are doing the wrong thing. This means that we do not want to read what he says about us and avoid him.
You've been hearing it incorrectly. The name is Moreh Zayin - the teacher of armaments. This is a metaphor for all those teachers who tell you not to do things because someone else may misunderstand you. These teachers stand with "virtual weapons" and give you a guilty look, so that you don't do what's forbidden.
Moreh Zayin come in different forms and they aren't necessarily school teachers. A parent who gives you a guilty look is also a Moreh zayin.