Reaction can only take place when there is resistance to action.
Earths atmosphere acts as a resistance so rockets exhaust can push off against it resulting in rocket flying off. In space there is no resistance due to it being vacuum so action from rockets exhaust can't cause reaction so rocket will get stranded in space. Its that simple.
The problem is nobody takes resistance into account, most people seem to think action reaction is all that takes place.
This picture for example:
All you see is action and reaction being shown in the picture which is slightly misleading. What most people don't seem to get is that reaction is taking place because the wall is resisting the action.