These elements are called Alkaline Earth metals because of two reasons:
Their oxides exist in earths’s crust and are very stable to heat. ( That’s why the word “Earth” is used)
Their oxides and hydroxides show basic (alkaline) natures.
Beryllium fulfills the first criterion but not the second one, since its oxides and hydroxides show amphoteric behavior, rather than alkaline.
So, it is not considered an alkaline earth metal in the true sense, even though it does resemble them in various other properties.
So, if asked which group 2 metal is not considered an alkaline earth metal, then your answer should be beryllium.
Otherwise, you should probably consider beryllium as an alkaline earth metal.