Probably because Firefox checks to see if you have the latest flash update.
Also make sure you have the latest Firefox update.
Click Help and about on the top menu of Firefox to make sure you are at 34.0.5
I thought Youtube doesn't require flash anymore when their site is used directly.
I have no flash player or any Adobe software yet I can use Youtube through Firefox.
I can't play Youtube videos embedded in other sites, however, those do require flash.