I randomly found myself thinking about why Snape got so upset when Phineas Nigellus called Hermione a Mudblood in Deathly Hallows. (p. 689 Harry Potter and the Deathly Hallow)
"'Headmaster! They are camping in the Forest of Dean! The Mudblood—'"
"'Do not use that word!'"
"'—The Granger girl, then, mentioned the place as she opened her bag and I heard her!'"
It was infinitely harder than even he had imagined it would be to follow the Dark Lord's orders while also following Dumbledore's. Hogwarts was not the same without Dumbledore meddling in every corner and even though Severus could barely tolerate his antics; he was the only man who had never questioned his allegiance. And now he was gone. He had promised Dumbledore that he would do his best to protect the students of Hogwarts, and he was doing everything he could while still upholding his guise as the Dark Lord's servant. Instead of letting other students administer Unforgivable Curses as punishment he gave lines and, except for the Carrows, he allowed the retention of all the professors, and unbeknownst to anyone else he sent the house elves to the rooms of punished students with essence of dittany.
But now Dumbledore's portrait was asking him to do the near impossible, give this sword to Potter. No one, least of all himself, knew where Harry and his golden trio were. He had caught Potterwatch a few nights by fiddling the dials on his radio and muttering words related to the Order, but those snarky Weasley twins only had words of hope for Harry, "wherever he may be." Snape couldn't say that he was concerned for Potter and his friends because he knew that Ms. Granger's intelligence and quick thinking would prove as useful to them in the world as it had once done at during their many incidents at Hogwarts. He did, however, hope just as much, if not more than anyone else that this war would end so he would finally be at peace. He wasn't delusional; he knew that no matter what the known status of his true allegiance was he couldn't hope to survive.
He knew that besides watching over the well being of the students for as long as possible his must important task was to get the sword resting atop his desk to Potter. Even though he didn't understand why; somehow Potter needed this sword to defeat the Dark Lord. He was putting away his radio one night after a seemingly futile attempt to find Potterwatch again when he was interrupted by Phineas Nigellus' portrait. "'Headmaster! They are camping in the Forest of Dean! The Mudblood—'"
"'Do not use that word!'"
"'—The Granger girl, then, mentioned the place as she opened her bag and I heard her!'" He nodded at him in thanks and turned to speak to Dumbledore's portrait, still perturbed by Phineas' carefree use of that word.
The man lived in the past, a past where prejudices based on blood were more commonplace, and a past to which Snape himself used to belong. He heard that word used so often at home as a child that when he met Lily Evans he was mesmerized by her because she was a very talented witch. The two things weren't supposed to go together, Mudblood and magically gifted, but there was no denying Lily's power. He made the mistake, just once, of calling Lily that horrible word and the loss of their friendship was enough for him to vow never to speak it again.
Mudblood was not a suitable word for anyone, but it was just as unsuitable for Lily when he let it slip that day down by the lake as it was for Hermione Granger. "The smartest witch of her age," he scoffed. But it was true. Hermione Granger, while an insufferable know it all, is a very talented witch. He had noticed her skill in her first Potions class and instead of mollycoddling her like the rest of the teachers, he chose to challenge her, to further her intellect.
It's true, not many can understand the subtle science of potion making, but of all his students Ms. Granger held the most promise. She took the time to study, perfected spells, and understood why certain ingredients worked together to perform tasks. He didn't praise any student not in Slytherin house, however, and so her work remained graded harsher than anyone else's and her effort under appreciated. And it would remain that way. Despite his performed cruelty towards the girl, he is aware that she is currently somewhere in the Forest of Dean sacrificing her safety for the good of the Wizarding World and she may be the most gifted witch to have graced Hogwarts' halls since Lily Evans herself, and for that he would not have her called that horrible name in his presence.