I just noticed that in a certain usage, the phrase-forms ‘hang … off …’ and ‘hang … on …’ mean the same thing. (Of course, you could find a lot of examples of such phenomena in English, but hey, this is my blog and I reserve the right to post about things that are not very new or original.)
‘Course, you wouldn’t say ‘hang the shirt off the hanger’ or ‘hang the keys off the hook’, but you would say ‘hang the Payment object off the Speaker object’ or ‘hang the new tree off the first leaf’ when talking about data structures in software. Or at least, I and my peer group would say these. But they mean the same as if you replace ‘off’ with ‘on’. I guess the preposition there is more for looks than function, since ‘hang’ itself is fairly unambiguous.
So I guess the only thing that’s actually interesting about this is that the phrase was appropriated into programming terminology, then slightly morphed from its origin, and probably for no good reason.