How would you understand if I say
He is not a teacher.
He is no teacher.
He is not any teacher.
How would you understand if I say
He is not a teacher.
He is no teacher.
He is not any teacher.
Number 1, "He is not a teacher," suggests only that teaching is not what he does. It might mean that teaching is not his job. It doesn't necessarily suggest any kind of insult.
Number 2, "He is no teacher," sounds like a judgment of something that "he" has done. Perhaps he tried to teach (or his job is to teach), but he's not good at it. It's like saying, "He shouldn't call himself a teacher, because he's terrible at it."
Number 3, "He is not any teacher" sounds awkward, and I'm not sure how I would interpret it. If you said, "He is not just any teacher," I would take that to mean that he is a very special teacher in some way (e.g., he won a teaching award, or he received a Nobel prize, or he is the most popular teacher in the university). One would usually say, "He is not just any teacher; he's the teacher who ...[whatever he did that was special]."
I hope this doesn't make things more confusing, but sometimes "not, no, and not any" can mean exactly the same thing. If I say, "I do not have money," "I have no money," or "I haven't any money," they all mean money is something that I lack. So context is very important.