I don't understand a thing.. Snape is the half blood prince, so why is he a Slytherin, if he doen't have pure blood?

Slytherin house is againts anyone who's not born from magical blood ie muggles and muggleborns. As a half blood has at least one magical parent, they are accepted into Slytherin.

I don't think it was necessary for a Slytherin to be a pure blood.That was just another Slytherin trait,like pride, ambition,cunning etc.Not all Slytherins can have all these traits.That also happens in the rest of the houses.Voldemort was a half blood,but he became a Slytherin as well.

Why?!...because he is SEVERUS !!! :))))))))))))))))))))))))))
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Slytherins are, according to the Sorting Hat, devious, secretive, cunning, and ambitious. The blood purity thing was not started at Hogwarts in itself, so far as I know. Quite possibly, when the hat saw Snape's mind, it could see his secrecy and cunning. The Sorting Hat can't tell if you're a pure-blold, half-blood, or Muggle-born.

It isn't because you're a half-blood or muggleborn that you can't be in slytherin. The sorting hat doesn't take account of the *purity* of your blood when he is choosing which house you will most fit in, but your values. If you are ambitious=slytherin, brave=gryffondor, hufflepuff=loyal, ravenclaw=clever. There are some muggleborns in slytherin but because of the majority of slytherins that have prejudice against them they tend to have low profile, to not be noticed. Because the don't want to be bullied. So please no. Just because you're a slytherin doesn't mean you can't be a muggleborn or half-blood.

Because he is so awesome he brain-fried the sorting-hat into putting him in Slytherin. Jk, he was probably just a Slytherin at heart. :P

You don't need to be pure blood to be in slytherin. You can also be a half blood, but not a muggle born. Voldermort was half blood and slytherin too.

SALAZAR Slytherin was pro pure blood. (although there is some evidence that he is madami tolerant towards half-bloods being that the basilisk went after muggleborns. But that could just be Voldemorts view).

Regardless, Hogwarts itself (including the Houses and the sorting hat) does not base anything off of "blood" status. Students are sorted based on their traits. And quite frankly, Snape is very "Slytherin" (sly, cunning).