Why does 腰抜け mean coward? Why does mean coward? I see (waist) + (missing/losing) = (coward), but I fail to see how they add up.

Looking at the Daijisen definition, it seems to mean in the first definition "losing the strength of the back/waist and becoming unable to stand", and probably from that in the second definition "lacking guts"/"coward".

I would say from this that `` might be very close to the English expressions "spineless", "no spine", "lacking spine" etc for a similar reason.