How is Harry a Half-Blood?

Because his mother was a muggleborn. You are a halfblood when one of your parents is a pureblood and the other is either a muggleborn or muggle
From wiki:Half-blood is the term commonly given to witches and wizards who have both magical and Muggle heritage. As pure-bloods claim to have no Muggle ancestry whatsoever, those who have and acknowledge their Muggle as well as their wizarding heritage would be considered half-bloods. By the 1990s, half-bloods were the most common type of magical person, as the wizarding population would become extinct without inter-marriage with Muggles and Muggle-borns.

he is half blood coz his mother is muggleborn so couldn't be regarded pure blood! but if we wanted to be accurate, we can say he's 1/3 blood or sth..:D but he still doesn't have pure blood..

no, his mothers parents were no wizards/wiches

He's half-blood because his mother was muggle born (mudblood) and for people like Malfoys it was the same as she was a muggle, so that's why Harry is a half-blood.

harry is a half-blood cuz is father is pure-blood but his mother is a muggle-born

Cute! and sad!

For some wizards (Like the Malfoys) a person like Hermione is a muggle. So that would mean some would say Lily is a muggle. If this was true, Harry would be a half-blood. But that's just the their way of thinking. In J.K.Rowling's books, Harry is a pure-blood regardless of what the Malfoys think. Hope that helped :)

That clears everything up. That question has been bothering me ever since I read the books.