As we all know, Book 7 is due quite soon. Day after my birthday, in fact, which is really quite nice. So this post is a sort of anticipatory celebration.
Really it should be "Harry Potter and the part-human," but Rowling deals with it all: non-, part- and post-humanity. This theme has grown in the series right along with Harry, Hermione and Ron; as they have matured, this dark element of the wizarding world has become more and more prominently the source of the evil Voldemort represents.
It begins with a simple distinction between wizards and witches, and non-magic people: Muggles. It's not, I think, insignificant that we poor non-magical slobs have a label, though not necessarily mean-spirited (one can imagine it being said affectionately). But this divide is absolute. One is Muggle or magical; one lives in the Muggle world, blissfully or otherwise ignorant, or one lives in the entirely separate magical (=real) world as a witch or wizard.
Unless you're a Squib: the in-between people who do not inherit magical ability but who remain a part of the real world. That Rowling introduces this in-between category is indicative of her penchant for complexifying the initial simplicities of the early books. I like this.
What's interesting is that although these distinctions and categories and derogatory labels have real force, Muggles, Squibs and non-pure-blood wizards (as Rowling's term is clearly analogous to the n-word, which I cannot bring myself to say or write, I will avoid it as well) are all considered obviously human.
But not everyone is human. There are part-humans, including Hagrid, the centaurs, Lupin the werewolf, and vampires. And there are non-humans: goblins, giants, house-elves. What we begin to see most prominently in the fourth book, with Hermione's creation of S.P.E.W., is that there is a huge and until now mostly hidden problem in the wizarding world: the unquestioning assumption of the superiority of wizards over other kinds of beings.
And it is this very assumption that, carried to its logical conclusion, leads straight into the pure-blood mania that serves as the rhetorical appeal of Voldemort and his followers. The echoes of Hitler and Nazism are hard to miss.
But Voldemort tells Harry as early as the second book that he is no longer concerned with the goal of pure-blood wizard ethnic cleansing. Voldemort's real goal is the attainment of immortality. This ambition, and fear, is what makes Voldemort the posthuman figure. Human, for Voldemort, is synonomous with mortality, the enemy. And so all humans are to be despised--not simply mixed-blood wizards and Muggles, but everyone. He alone is the enlightened and powerful one.
What I would anticipate most about the seventh book is how the different threads of this theme will come together and prove to be the basic conflict between the Order and Voldemort and the Death Eaters, the thing that distinguishes the good from the bad: who is willing to accept the Other in all its varied forms, and who is determined to annihilate them?