neither fish nor fowl
Also, neither fish nor flesh; neither fish, flesh, nor fowl. Not one or the other, not something fitting any category under discussion. For example, They felt he was neither fish nor fowlnot qualified to lead the department, yet not appropriate to work as a staff member either. This expression appeared in slightly different form in John Heywood's 1546 proverb collection ("Neither fish, nor flesh, nor good red herring") and is thought to allude to food for monks (fish, because they abstained from meat), for the people (flesh, or meat), and for the poor (red herring, a very cheap fish).
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