I have to correct myself, there is some confusion regarding patriarch, the official etymology says "founder of the family" from Ancient Greek πατριά (patriá, “generation, ancestry, descent, tribe, family”)

From Middle English patriark, patriarche, from Late Latin patriarcha; later reinforced by Old French patriarche, from Byzantine Greek πατριάρχης (patriárkhēs, “the founder of the tribe/family”), from Ancient Greek πατριά (patriá, “generation, ancestry, descent, tribe, family”) + -ᾰ́ρχης (-árkhēs, “-arch”), with some senses likely influenced directly by Latin pāter (“father”) or Ancient Greek πᾰτήρ (patḗr, “father”). Compare matriarch. Surface analysis patri- +‎ -arch.

Tho the similarities between patria and pater are certainly not accidental.

So bottom line, patriarch is less gender specific than pope.