A letter from Steve Jobs about why they don’t allow Flash on iPhones, iPods, and iPads. (Notice he specifically uses the harsher “allow” instead of the much softer “support”.)
Jobs sort of circles around the main issue which is, from my own perspective as heavy web user and web developer: though Flash may have been necessary in the past to provide functionality in the browser that wasn’t possible using JS, HTML, and CSS, that is no longer the case. Those open web technologies have matured (or will in the near future) and can do most or even all of what is possible with Flash. For 95% of all cases, Flash is, or will soon be, obsolete because there is a better way to do it that’s more accessible, more open, and more “web-like”.