I think that Clements is an author skilled at creating school stories. He expects kids to recognize relationships with the teachers they had that were tough, but from whom they learned the most. I personally am this kind of teacher. Students often fret under my reign, but they usually thank me later when they realize how well I prepared them for what was to come.
I think that the author wants the reader to understand the antagonism and potential for rivalry that exists between Nicholas and Mrs. Granger. It seems to me that this is what the exposition helps to reveal to the reader. We never get the idea that either one of them intensely dislikes or has disdain for the other. Rather, we see their relationship as one where each holds an almost equal level of magnitude. This ends up playing into the resolution of the novel when Mrs. Granger recognizes how the invention of the term "Frindle" gains a life of its own and she does not wish to stand in the way of the story, but rather seeks to enhance it.