In the wizarding world of Harry Potter, the term "half-blood" is a bit more complex than it may seem at first glance. In the universe of the Boy Who Lived, this term refers to a wizard with both magical and non-magical (Muggle) ancestry.
Harry Potter is considered a half-blood because his mother, Lily Evans, was Muggle-born (born into a non-magical family), while his father, James Potter, was a pure-blood wizard. This gives Harry a mixed lineage.

Likewise, Albus Severus Potter, the son of Harry and Ginny Weasley, is also classified as a half-blood. Although his mother, Ginny, comes from the pure-blood Weasley family, blood status is passed down through the parents.
Since Harry is a half-blood, his children, including Albus, also inherit this status. Therefore, even with pure-blood ancestry on his mother’s side, the mixed heritage of his father determines the blood status of his descendants. However, teasing him for it at Hogwarts would be unlikely — considering who his father is.