I'll give the serious answer, because apparently nobody else wrote it.

Bear cavalry is a no-go for about the same reason that we do not raise bears for meat. After all, a bear can be fed with just about anything, and grows quickly, and thus _should_ be a good source of food. But it has a big drawback, which is that bears don't tolerate well other bears. You cannot make a herd of bears (however awesome it would be). There is a nice analysis of the conditions of domestication of animals for food production in Jared Diamond's [Guns, Germs and Steel][1], which cites several animals as counter-indicated, for various reasons. Bears are the example of an animal that you cannot put in groups.

Of course there are other reasons why bear cavalry would be challenging, as cited in other answers: management of hibernation, difficulty of fitting a saddle on an animal whose weight can triple over the year (they really thin a lot during hibernation), possible low tolerance of the spine to the pressure from a rider... but all of these could probably be overcome. The impossibility to keep bears together is a much bigger problem, which prevents assembling a significant bear cavalry squadron. At best, you could have a couple of scouting bears.

(Bears are remarkably good at moving across difficult terrain, so they could make good scouts in mountainous areas.)


  [1]: https://en.wikipedia.org/wiki/Guns,_Germs,_and_Steel