I tried one time, as part of an experiment, to ride a bike with a fixed handle bar. Impossible. So, in any case, our movements made with the handlebar helps us in not falling down. I can feel kinda how, but cannot really put a finger on it. Does anybody know the answer?
You can't ride it because it's very thin and so is bound to fall over to one side or the other.
A more difficult question is why you can ride a bike in normal circumstances. That has already been discussed on this site but as you would expect the answer is related to the steering mechanism.