Harry Potter is…a problem. Voldemort has managed to ignore the problem thus far, focusing more on the other students in class and pointedly not looking at names while grading homework assignments—he's even gone as far as to ask students to come and claim their own work because he refuses to acknowledge Potter.

If he acknowledges Potter, he will have to acknowledge his undying hatred for him, and if he acknowledges that, then he might be biased against the boy. Voldemort is many things, but an unfair teacher is not one of them, so he simply…doesn't look at Potter. When the monthly student evaluations come back, Potter is not on the list of students who are doing poorly in his class. As far as he's concerned, this is a win-win situation—Potter gets an education, Voldemort gets to provide an education, and no one ends up stabbed, beheaded, de-limbed, or otherwise maimed.

Quirrell watches this all happen, a peculiar feeling swirling in his head. He asks, "My Lord, why do you allow the Potter boy to live?"

"He is my student."

"But he killed you."

"But he's my student."

"But he's destined to be your undoing!"

"…But he's my student," Voldemort stresses. "I can't murder a student, that would be very disruptive to the safe learning environment I'm trying to foster."

"You would be much more able to foster that environment if you could get your fated bane out of the way," Quirrell points out.

Voldemort considers this carefully. He looks at it from every possible angle and, he must admit, there is sense in Quirrell's words. However… "Think of how mentally bothersome the murder of a classmate would be," he despairs. "It would surely affect their grades in the upcoming exams! And think of what it would do to the Granger girl…she's one of my most brilliant students, I refuse to let something like trauma stop her from reaching her full potential. And the Weasley boy—well, he's not exactly studious, but he has potential!"

Quirrell is silent for a very long time after this. Then, "Isn't the Granger girl a muggleborn?"

Voldemort says, "Oh. I forgot about that."

What he means: he forgot that he is supposed to care about blood purity, and now that he thinks about it, he can't quite bring himself to find it all that important. What Quirrell hears: Voldemort forgot that Hermione Granger is a muggleborn.

Quirrell says, "Well, now you remember." Just like that, the conversation is over.

They draw two very different things from the discussion. Quirrell is satisfied that his master is going to return to his ideals, possibly terrorizing the mudbloods along the way.

As for Voldemort…well, persecution isn't conducive to creating a safe learning environment, is it?

A/N (posted on ao3 2022-11-03): Voldemort is a bad person but a responsible teacher