They forgot ayumi......

[Andrenekoi]

From wikipedia:

In Japanese culture, idols (アイドル aidoru?) are (usually female) media personalities in their teens and early twenties who are considered particularly attractive or cute and who will, for a period ranging from several months to a few years, regularly appear in the mass media, e.g. as singers for J-pop groups, bit-part actors, TV personalities (tarento), models in photo spreads published in magazines, advertisements, etc.

If i got it right, Idols are multimidia celebrities whose image and life style has a bigger impact than their works...
Maybe they considered that Ayu's career is music focused instead of multimedia (she doesn't act in dramas and movies, she doesn't have a tv show anymore and even if she has some photoshots, I don't think she could be considered a model), or that her work has a bigger impact than her image or life style...