Why does a helium balloon fly?

Unfortunately your answer is wrong.
Because the air both on the right and the left side of the balloon is equally high, the atmospheric pressure on both sides is equal. That means: The force acting on the balloon from one side equals the force acting on the ballon from the opposite side. These forces cancel each other out.

To make the balloon move in a certain direction, a lateral force would have to be greater than the other one.
But this is not the case.