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Slytherins believe in the importance of taking care of their own. Everyone else is a person, but so are they, so a Slytherin’s job, before everything else, is taking care of them and theirs. This makes what Slytherin are known for, their ambition and ruthlessness, stand out strikingly even while a Slytherin’s core is not inherently selfish or cut-throat.
All of the Houses contain people with great ambitions and great desire for accomplishment and the furthering of their goals. Gryffindors will take on the world to do what they think is right, and are willing to make sacrifices and overrule those who would compromise on what needs to be done, and that’s nothing if not ambition. What makes the Slytherin ambition stand out so significantly is that it’s seen as a selfish ambition, and a guiltlessly selfish one at that. That drive is tied to personal achievement instead of idealistic achievement, and that makes it easier to point at.
But this is key: selfish ambition is idealistic ambition for a Slytherin. A Slytherin’s first priority is to their loved ones not because they love deeper or harder than the other Houses (they don’t), but because it is wrong to betray or abandon your people and right to defend and promote them. Loyalty and defense of your own is an inherent part of the Slytherin morality.