The monkey house
I should have added in this morning’s post that primate also derives from the Latin primus (first) and primas (of first rank). The term in biology speaks to our species-centric belief (or vanity) that we and the species most closely related to us are of the first rank.
A primate is also, in theological terms, a first among equals, such as bishops. So a reference to an Anglican primate does not necessarily identify a great ape.