"Why would that be the case?" Hermione asked, before Harry could figure out his own question.
"The Headmaster of Hogwarts is a powerful position, for Wizarding Britain as a whole. His family alliances become Hogwarts', and his House is likely to view Hogwarts as their own demense; a powerful position worth holding. As such, they would often vote to enrich Hogwarts, in order to burnish their House's glory."
Harry's brow furrowed slightly, "Wouldn't that mean that Hogwarts would also inherit a Headmaster's familial enemies?"
Snape nodded, once. "Naturally. As Headmaster of Hogwarts is a coveted position, it has rarely gone to a House Besieged."
"Besieged?" Hermione prompted.
Snape sighed, softly, "All Houses have allies and enemies, it is merely human. However, in the general scheme of things, the two tend to balance out. A House that enrages its enemies is one that will suffer attacks from all sides. Even their allies may not guard their flanks."
Harry could see it, in the manner of an analogy; as if he was standing on the battlefield - the stag beset by wolves from all sides, horn and hoof and kick not enough to defend himself.
"How often have Headmaster's put their own house ahead of their position as Headmaster of Hogwarts?" Harry asked, only midway through realizing he was speaking. Hermione had this funny look on her face, as if she was surprised Harry was asking intelligent questions.
"Enough," Snape said, "To their everlasting detriment."
Hermione and Harry didn't need to ask the question, their widening eyes asked it for them.
Snape, atypically, responded, "Those foolish enough to assume that Hogwarts does not have any defenses against venality, may find their very being incorporated into the defense. Those ghosts who walk the halls... some are not as natural as you might imagine. Neither their deaths nor their unlife."
Harry was not surprised, not one whit, at the air of dark satisfaction that emanated from Snape. Magic itself may not be good or evil, but in a magical world, there were many traps for the unwary.
Snape said sternly, "Those raised in the Muggle world step into the Magical one as fresh-faced as mewling babes. Most have the wit to either ask or avoid the finer points of Wizarding culture."
Snape's eyes raked over both of them, "Not you lot, though. Not for a moment did you stop and reconsider your own prejudices." Snape was moving, circling. Harry and Hermione's heads spun to keep up with him. "Not once did you consider that Malfoy - or Crabbe or Goyle - might have been justly proud of his lineage, of his House." Harry refused to turn around - it would show a level of fear that was unacceptable. Snape was teaching, after all. "You allied yourself with Ron Weasley, the least formal of a Family infamous for its... modernism." Snape shot them a sidelong look, still moving widdershins. "Or, did you think, that Daphne Greengrass would have dared to say even a single spiteful word about her equivalent of Aunt Muriel?"
Snape's voice had dropped to a low purr, "My sources tell me that both of you are considering a career in the Ministry. If you cannot acquire the wit and elocution necessary to navigate a foreign culture - what makes you so certain that you are qualified to lead it?"
Hermione already had her mouth open, though Harry was hardly listening, at this point. This was how a Slytherin thought. Working for the ministry was not about public service, it was about shaping their world. Given that, it was hardly surprising that Wizards wanted to be certain that foreigners understood the barest basics of their society before proposing reform.
[a/n: Intelligent isn't the right word, Hermione dear. Canny is.
I do realize that venality is a stronger and less general word than thievery. I use it because it sounds so good. You're welcome.
Snape does not often make the case for learning his classes well. Granger and Potter have been out of line, and calling them on their bullshit is satisfying.
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House and Family are equivalent, by the way. House is used for the Founders' Houses because it was how they wrote it. Family, if they'd used that word, may have resulted in minor blood-bonds to foster familial bonding. So let's be glad they didn't!]