I have to admit, I like my Ne, but I am not entirely sure that it is the best function to teach something unless it is to a person that also uses Ne. :) It has its own good and bad points.
I think the most noticeable thing about Ne teachings are Ne jumps. I had a teacher last semester who had them a lot. His assistant, when trying to figure out what he talked about, looked at his slides and was staring at him. I remember that I helped him with the notes and while he was presented, he apparently did not get how could he came from that slide to talk about these things. Not to mention, I talked to some of my classmates and some of them were unable to follow the jumps.
But for me, as an INTP, these jumps always followed some sort of connection. I could not always predict them, which is what made them fun. Many new ideas to learn.
Which not that I think about would have explained why some were annoyed by it.
I could even saw these same things in myself. When I was trying to help my sister with the chemistry in primary school, I apparently used things from concepts from quantum physics to philosophical problem. Let me tell you that my sister actively refused my help with studying for years after that. Apparently I just confused her.
Which can also lead to these teachers seeing unprepared. For example, when I was an English teacher in Eger, I always prepared the plan for my lessons. I was to be used if I could not come up with something on the spot. 80% of these plans were never used.
Which might be the reason, why when I asked for the way to improve, the only point that I could ever get was to prepare for my lessons. Which was not helpful, because I did. I once even showed my plans. Still, I appeared unprepared, because I did not use them.
But these things also have positive sides. The first is, that because Ne sees all the connections, if there is a connection with the matter that the person already knows well, then this can be used to try and explain the subject in a more accessing manner. And there are a lot of connections, so there is never a lack of possible explanations. If one does not work, then another one will.
The second is, that it makes the lessons so much more fun and engaging. Some of the most fun lessons I have been to have been thought by people that had Ne in the first or second place. I could see, that they are clearly interested in the subject matter and they actually shewed their enthusiasm. Though I am worried for some that they might be workaholics.