Spaceships in atmosphere are usually depicted as flying due to downward force from an engine, like a hovering harrier. Since the Franklin wasn't designed to fly in atmosphere, it may not be able to direct sufficient force in a downward direction to effect a vertical takeoff.
So, if it can't just take off straight up, it must need to generate lift a different way. Assuming that the ship is producing lift via Bernoulli's Principle and an airfoil, needing a jump start makes perfect sense.
The lift generated by an airfoil is dependent upon the speed at which the craft is moving through the air. This means that the craft needs to get going fast before it can actually fly. This is why commercial aircraft require long runways, so they can get up to speed. As you may have noticed, there was no runway in front of the Franklin.
Therefore, before the ship could fly under its own power, it needed to get going fast enough that the stabilizers could keep it flying, despite providing minimal lift on their own. This required falling off a cliff.
In other words, it's just what Chekov said:
We have to achieve terminal velocity in order for the stabilizers to provide lift.