A rhetoric term I never heard before. A logical refutation, especially one that disproves a
proposition, by proving the direct opposite.
It's been a long time since The Forest of Rhetoric has been mentioned. Newcomers may
enjoy browsing:http://humanities.byu.edu/rhetoric/silva.htm

Very much off-tangent. (Sorry, Bill)

But elenchus makes me think of echida for some odd reason...

Let's see. Why? There's the echidna; and the platypus; and the e-chidna again; and, of course, the missing lenk. That must be it, misspelling excused!

E-Len-Ch-us.

Is this a rhetorical term that came from down under and transmuted itself in flying up to the British Isles?

And elenchus made me think of entelechy, but I couldn't define it.

entelechy ,
pl. entelechia < L < Gr entelecheia, actuality < en telei echein < en, in + telei, dat. of telos, end, completion + echein, to hold: see SCHEME
1 in Aristotelian philosophy, the actualization of potentiality or of essence
2 in vitalism, the inherent force which controls and directs the activities and development of a living being

Well, an echidna is a living being, so I s'pose we could discuss the entelechy of the echidna punctuating the discussion with an elenchus here and there...

My guess is there is some relationship with the Italian word "elenco" = list
Perhaps a list of arguments against...who knows

1 in Aristotelian philosophy, the actualization of potentiality or of essence
2 in vitalism, the inherent force which controls and directs the activities and development of a living being

What a great word! Almost as good as serendipity

"Serendipitous entelechy" sounds nice, though I suppose it's a tautology of sorts.

some relationship with the Italian word "elenco" = list

Perhaps, by some twisty trail. My AHD says elenchus is from Latin from the Greek, elenkhos, refutation from elenkhein, to refute. I suppose the word could have become, in Latin, to mean an argument in steps, and then come to mean the steps themselves, hence, a list.