Interesting origin as people have described, but I always understood it differently. To me pull yourself up means to motivate yourself to do something, similar to pull yourself out of a hole or get yourself out of trouble. By your bootstraps I understood to mean to take the first step towards doing something, so doing up your boot straps or laces basically and getting on with it. So to pull yourself up by your bootstraps always meant to me to get yourself out of a difficulty by your own efforts, nothing to do with the task being impossible. I’m British so maybe the meaning is different here.
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