E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
It is neither fish, flesh, nor fowl; or Neither fish, flesh, nor good red herring. Not fish (food for the monk), not flesh (food for the people generally), nor yet red herring (food for paupers). Suitable to no class of people; fit for neither one thing nor another.
Fish comes first because in the Middle Ages the clergy took precedence of the laity.
She would be a betwixt-and-between . neither fish nor fowl.Mrs. Lynn Linton.