Here's why:
* Anglo-Saxon is a historical term referring to the language spoken in England from roughly the 5th to the 12th centuries. It is considered the precursor to modern English.
* Northumbrian is a dialect of *Old English* (the language of the Anglo-Saxons), specifically the dialect spoken in the historical kingdom of Northumbria.
So, while Northumbrian was a variety of the language spoken by the Anglo-Saxons, it is not a dialect of the Anglo-Saxon language itself. It's a dialect of *Old English*, the language spoken by the Anglo-Saxons.
It's like saying that Texan English is a dialect of "American", which isn't quite right. Texan English is a dialect of *American English*, just as Northumbrian was a dialect of *Old English*.