Why do they call Harry a half-blood and say that Lily and James were both exceptionally good students at hogwarts?

James is a pureblood. While Lily is a muggle-born. Which makes Harry a half-muggle hoặc halfblood
Being a half blood is because of your parents' status.
bạn đã đưa ý kiến in the other answer that he should be called pureblood because his parents are both wizards.
Pureblood means your ancestors, ALL of them, doesn't have a tint of muggle-blood.
When there's a half blood hoặc muggle born in your ancestors, that automatically means that bạn are a HALF BLOOD.

Those are the three blood statuses of wizards:
Pureblood- there are no Halfbloods hoặc muggle borns in your ancestors
Halfblood- there is a halfblood hoặc muggle born in your ancestors and
Muggle-born - bạn are born from two muggles. which means there are no wizards in your family.

Examples are:
pureblood- Ron Weasley, Draco Malfoy
halfblood- Harry Potter, Voldemort/Tom Riddle
muggle-born- Hermione Granger, Lily Evans

Harry is a half-blood because his father James was a pure blood wizard and his mother was a muggle born witch. Lily had magical powers but both her parents were Muggles. Being a good student (or a powerful wizard/witch anyway) has nothing to do with blood status. For example, Hermione has Muggle parents like Harry's mother, but she's the best student at Hogwarts. Far better than Ron and Malfoy,who are both pure bloods.

Harry isn't pureblood, because Lily is a muggle born. Because of that, he doesn't have completely wizard blood.