There's a lot to hate about Flash video. And yes, I'm aware of the irony of saying this when I myself put Flash videos on my blog. If YouTube would use a decent format, I'd be onto it so fast your head would spin.
It's not a fully open standard, making it near impossible for anyone to create Flash applications that don't depend on Adobe. There are a zillion movie players for .avi, .mpg, and even a handful for .mov, there's only one player for Flash .swf applications. (In fairness, mplayer can, sometimes, play .flv videos. mplayer is awesome!) That's a warning sign of data obsolescence.
Specifications for the Flash formats are only released to developers on the condition that they don't create Flash players. Flash videos contain executable code, which is a serious security hole: it's only a matter of time before somebody creates a virus which runs through Flash, even on Linux. Most Flash applications are poorly written, with terrible user interfaces and buggy implementations: Flash sites frequently lock up my browser. You can't index or search Flash sites, or copy text out of them, and if you are blind and use a screen-reader, web designers who use Flash are giving you a big F-U. And if you're a movie creator, why on Earth would you be happy with the crappy, low resolution, compression-artifact-filled ugliness that is the typical .flv file?
I could go on, but I'll just link to one more reason to avoid Flash if possible: Adobe is now adding Digital Restrictions Management software to the format.
Finally, there's a classic suite of arguments against DRM that will be as true for online video as they were for music. DRM doesn't move additional product. DRM is grief for honest end-users. And there's no reason to imagine that new DRM systems will stop copyright infringement any more effectively than previous systems.