I regularly "push back" in my amphibious planes, whereas the floatplanes won't do it. It has to do with the wheels, I think. It's a strange quirk with FSX, that you can use the pushback function on wheeled craft (on the tarmac, or in the water), but the function doesn't work for a floatplane. The A2A cub supposedly allows you to "paddle" in the water, but I've never done it. Try an amphib, instead of the floatplane, and press shift+P to pushback. I don't think it has anything to do with missions either. I am working on building my third "Dispatch Mission", and never had a problem pushing back. What mission are you running, by the way? It may be disallowed, for all I know.