Something impermissible cannot be allowed. A school, a workplace, or a court may call an act impermissible: there is a rule, and this crosses it. It is a formal, often legal-sounding word. In daily talk people say not allowed, or you can't do that. Though actually, it is colder and stronger than “not nice” or “not a good idea.” Those are opinions. Impermissible means someone with authority has drawn a line.