The best explanation for the observation that the balloon appears to move backward relative to the car when the car starts moving forward is:
The car moves forward, while inertia keeps the balloon in place.
This statement accurately describes the effect of inertia—it is the tendency of the balloon to remain in its initial state of rest when the car starts to move forward that makes it seem like the balloon moves backward. Inertia is what keeps the balloon from immediately moving with the car, causing the relative motion observed.