Half the local food is not tough or oily (6)

I believe the answer is:

greasy

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'oily' is the definition.
('greasy' can be a synonym of 'oily')

I cannot understand how the rest of the clue works.

(Other definitions for greasy that I've seen before include "Like the pole that is hard to climb" , "Cheap 24" , "Oily or smeared with fat" , "Sticky with fat" , "Thickly oleaginous" .)

I've seen this clue in the Irish Times.

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