Have you ever tried shorting the +ve and -ve terminals of a battery using a thin wire? Go on, try it.
A battery is a voltage source not a current source. Don't try to short it !
A (ideal) voltage generator will keep the same voltage at its poles regardless the value of the load you put in parallel to it. From ohm's law the current flowing through the load R will be given by I=V/R. You can see that a short circuit (R=0) will lead to an infinite current while an open circuit will lead to a 0A current.
A (ideal) current generator, instead will keep the same current flowing through it. In this case the situation is exactly the opposite we saw with the voltage generator. Using the same load R, as before, now the current is fixed while the voltage across the load (and the generator) will depends from the value of R following the law V=R*I. You can see, now, that any finite value load, including the short circuit, can't affect the current but only the voltage (during a short the voltage will reach 0V). A open circuit (R infinite), instead, will cause the voltage going ideally to infinite.
Shortly:
Ideal voltage generator: voltage is fixed, no problems with any load except short circuit causing the current going to infinite
Ideal current generator: current is fixed, no problems with any load except open circuit causing the voltage going to infinite