'non-estrous' originates from the Latin prefix 'non-' meaning 'not' combined with 'estrous', which derives ultimately from Greek 'oistros' (via Latin/Neo-Latin), where 'oistros' originally meant 'gadfly, frenzy'.

'estrous' (also spelled 'oestrous' in British English) comes from Latin 'oestrus', from Greek 'oistros'. The adjective 'non-estrous' is formed in modern English by adding the negative prefix 'non-' to 'estrous' to indicate absence of estrus.

Originally 'oistros' referred to a 'gadfly' or 'frenzy'; over time the sense shifted to sexual excitement or rut (estrus), and the modern compound 'non-estrous' now denotes the absence of that reproductive state.