Yes, automation kills off one set of jobs - the ones being automated - but it almost always ends up with additional jobs being created in other ways, oftentimes to handle the increased production generated by the automated positions. Personal computers and MS Word effectively killed off hundreds of thousands of typist, transcription, and stenographer jobs, but you don't see all those former typists, transcribers, or stenographers sitting in the gutters. Some retired early, some no doubt went on to welfare, but most found other work to do.
As in finances, single entry bookkeeping presents a false view of the world. If you're going to count jobs killed off by automation, then you have to account for the jobs elsewhere created by it; otherwise, you're simply lying by statistic.