At the time, it was said to be because Flash was using too many cycles to be responsive on the iPhone, but I wonder if it wasn't a sensible security decision too.
It isn't like Apple had the ability to re-architect Flash for their platform. Not supporting Flash on iOS was a huge push towards HTML5 (and native iOS apps).
The push towards HTML5 stopped dead in its tracks once streaming audio and video became doable without Flash. There's so much more functionality Flash was capable of, functionality that isn't possible without a nearly expert-level understanding of Javascript.