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While talking about blood purity to Harry, Hagrid says this.
And it's codswallop, to boot. 'Dirty blood.' Why, there isn’t a wizard alive today that’s not half-blood or less.
The question In Harry Potter, what is the ultimate source of magicians and magic indicates that all Wizard families are muggle born at some point. So how did the concept of 'blood purity' arise, and what did Hagrid mean by 'Half blood or less'?