While it is true that a student could feel as weary as the teacher does in this scenario, it would make no sense for a student to utter any of the following lines:
“My pack of unruly hounds: I cannot start / Them again on a quarry of knowledge they hate to hunt.” Only the teacher could say “My pack of unruly hounds”; if a student uttered a similar sentiment about other students in her class, she would have said merely “that pack of unruly hounds,” while referring to the other students. And only the teacher could remark that he cannot lead the class to a “quarry” that “they hate to hunt.” Any student in the class is one of those being led, not leading, which only the teacher can do.
Also, it would be nonsensical for any student to say, “No more can I endure to bear the brunt / Of the books that lie out on the desks: a full three score / Of several insults of blotted pages and scrawl / Of slovenly work that they have offered me.” The “slovenly work” is offered to the teacher, not to another student.
Finally, the line wherein the speaker asks whether he should use up his energy to “burn the scroll / Of their insults in punishment?” demonstrates that only the teacher can be creating this little drama for only the teacher is in position to mete out punishment; students cannot punish other students for their lackadaisical, dog-like stubbornness.