Match patterns on list of Strings

Here is another one:

DeleteCases[data, _?(StringMatchQ[#, "A*"] &)]

I am not sure how to do this using DeleteCases, but you can still use the Select function:

Select[data, StringTake[#, 1] != "A" &]

which has the desired result.

Edit Actually, you can also use DeleteCases like this:

DeleteCases[data, _?(StringTake[#, 1] == "A" &)]

 Pick[data, StringMatchQ[#, "A*"] & /@ data, False]
 (* => {"CD"} *)

EDIT: As noted in YvesKlett's comment, since StringMatchQ threads over its first argument, we can also use

 Pick[data, StringMatchQ[data, "A*"], False]

 Pick[#, StringMatchQ[#, "A*"], False]&@data

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