Clearly, in an "ass-kicking contest", the object is to kick your opponent in the buttocks. If you only have one leg, it is very difficult to kick someone, which seems where the expression comes in.
Now, the one-armed juggler idiom doesn't really make sense, because you can juggle with one hand. I can do two regular sized juggling balls one hand, which while not impressive in any fashion, confused me as to the usefulness of the expression. Obviously there are talented jugglers like Jason Quick who can perform very complicated juggling maneuvers with one handed.
Still, there must be hundreds of expressions like this, someone should collect them all.
Yes, bear, same with paper-hanger. "Busy as a one-armed paper hanger" always meant really busy to me - and really talented! I've always found that hanging wall paper required three arms, at the very least!
I think "as busy as a one-armed juggler" is still a fairly useful (sorry) phrase. Though I guess its meaning could be antonymic (did I use that word correctly?) in that some might think (like me) that it means "really super busy," and others "not busy at all."
Without intending any offense, how does this phrase's problematic nature impact the similar phrase, "as _____ as a one-legged man at an ass-kicking contest"? I'm curious as one of my favorite crab-boat captains on Deadliest Catch says it fairly often. I've never seen or heard of an ass-kicking contest (unless you count boxing), so this seems a slightly more whimsical phrase in that it's an unlikely event to occur in reality. Whereas, as we've seen, there are some one-armed jugglers around (welcome, quickjuggler!).
You didn't coin it sionnach, it's in general use. In that sense an apology is not due to yourself, though I am sure it will be appreciated by many. I wish quickjuggler well in his endeavours and am thankful he brought this to our attention.