If one cares to look at the Welsh meaning of the name, it should be Cadair Idris, or Idris is Chair.
How the term Cader has been adopted over the years, is a mystery.
The name Cader or Cadair, is Welsh for Chair, and the meaning of the name refers to the Giant Idris who sits on top of the mountain in his chair.
It should be Cadair, not Cader.