As you said this is an archaic word, but some things never change (sadly)
Also in the olden days professional educators where suffering the destructive effects of bad classroom behaviour. I am not an etymological expert but the roots are something like this:
Cheil o � = archaic form of �child of �
pro = still used to indicate a professional
litic = <lytic> = suffix relating to decomposing/falling apart
CHEILOPROCLITIC was used to describe kids that caused even the most experienced and professional teacher to fall apart.
note: it has been suggested that it may also refer to the private -biological- children of a teacher who are suffering neglect because their parent suffered a breakdown due to bad classroom behaviour.