A good article by the man himself as to why Flash is not supported on iPhones, iPads and iPods, at http://www.apple.com/hotnews/thoughts-on-flash
But there is also a long history between Apple and Adobe as mentioned in the book by Walter Isaacson. This could explain the resistance by Steve Jobs to Adobe Flash.
Excerpt from Steve Job's Biography by Walter Isaacson's
To make this work, the iMac needed to have great video editing software. So Jobs went to his old friends at Adobe, the digital graphics company, and asked them to make a new Mac version of Adobe Premiere, which was popular on Windows computers. Adobe’s executives stunned Jobs by flatly turning him down. The Macintosh, they said, had too few users to make it worthwhile. Jobs was furious and felt betrayed. “I put Adobe on the map, and they screwed me,” he later claimed. Adobe made matters even worse when it also didn’t write its other popular programs, such as Photoshop, for the Mac OSX, even though the Macintosh was popular among designers and other creative people who used those applications.
Jobs never forgave Adobe, and a decade later he got into a public war with the company by not permitting Adobe Flash to run on the iPad. He took away a valuable lesson that reinforced his desire for end-to-end control of all key elements of a system: “My primary insight when we were screwed by Adobe in 1999 was that we shouldn’t get into any business where we didn’t control both the hardware and the software, otherwise we’d get our head handed to us.”