Why is Haman called andan Agagite and not an AmalekeyAmalekite?
In Megillas Esther 3:1 Haman is called the Agagite which I always assumed meant he was a descendant of Agag the king of the AmalekeyAmalekite in 1 Shmuel 15:8. His lineage is confirmed in Megillah 13aMegillah 13a as being a genetic descendent of Agag the AmalekiAmalekite.
ומה שילם לי ימיני דלא קטליה שאול לאגג דאתיליד מיניה המן
If the point is to tell us that Haman was an AmalekeyAmalekite, why not just say so explicitly?