When Hundert remarks that he suddenly realized Sedgewick Bell was cheating, he abruptly switches away from that very particular and urgent problem to say:
I had come to this job straight from my degree at Carleton College at the age of twenty-one, having missed enlistment due to myopia, and carrying with me the hope that I could give to my boys the more important vision that my classical studies had given to me. I knew that they responded best to challenge.
This is the beginning of a justification for an action he did not actually take, but its circumlocutory nature tells the reader a great deal about Hundert's character in all its complexity.
His reaction is first shock, in which he shies away from the fact of what is happening into general principles, then pity for Sedgewick, which he thinks may have come from "the humiliation we had both suffered at the hands of his father." This is followed by a determination to do his public duty by exposing Sedgewick despite his pity for the boy, telling himself that this will be better for the boy's character in the long run.
Hundert's determination quickly collapses in the face of the headmaster's blunt threat that if he does follow his conscience, he will lose his job. He then tries to justify his own compromise, as well as the headmaster's. This chain of emotions and reactions shows Hundert's humanity, weakness, and tendency to rationalize. He is a kind-hearted man, but lacks the strength of character and integrity he attempts to inculcate in his pupils, as well as the ruthlessness to attain a high position in the world for himself.