He hates his father and loathes himself, but mostly hates half-bloods because of how his life turned out. Besides, he's pretty insane to hate a whole race of people etc. so I don't think, as he's trying to take over the world, that he stops and says 'Hey, I'm a half-blood!'
It's a fabulous series, I'm sure J.K Rowling thought of this fact. ;-)