To be fair to the OP, needing a multi-entry Schengen visa for flying between two Schengen countries but transiting through another, would not have been immediately obvious to me, either. My excuse is that I'm fortunate to not need to think about visas for most of my travel - and if the OP didn't need a Schengen visa either, probably is in the same place.

As a few other posters point out, it's not just limited to careless travellers.