Origin of evertClassical Latin evertere from e-, out + vertere, to turn: see verse
transitive verbe·vert·ed, e·vert·ing, e·verts
Origin of evertBack-formation from Middle English everted turned upside down from Latin ēvertere to overturn ē-, ex- ex- vertere to turn ; see wer-2 in Indo-European roots.
(third-person singular simple present everts, present participle everting, simple past and past participle everted)
From Latin evertere, from e (out) + vertere to turn around in various senses; hence in English: to turn about or overturn. In the 16th century the word appeared in the sense of upsetting or overturning; since the 18th century the sense of "turning out" like a pocket has been the dominant usage.