but only those few who understand what the heck it means

I confess I am one of the many who doesn't understand what it is, Father Steve.

A "rhinotomy" is defined as an "Incision into the nose" so I assume a "rhinectomy" is the removal of the nasal passage [in the same sense that an "appendectomy" is the removal of the appendix].

If a "facial" is a treatment which improves the appearance of the face, then I presume an "anti-facial" is a treament which disfigures the face.

On this basis, an "anti-facial rhinectomy" would seem to be an operation which disfigures the shape of the nose, presumably by removing the nasal passage.

Anyone who survived an "antifacial-rhinectomy" would have to breath exclusively through the mouth, like a 'mouth-breather', a slang term for a person as stupid as a goldfish or other mouth-breather.

Very clever, Vernon.