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well,, when you push forward, your foot has to push off the ground in order for your body to overcome inertia and move forward .. the ground is heavy and stable so your body moves forward ,,, in your case your are in fact pushing the boat backwards, because there is very little friction Between the boat and the water and the boat is light and unstable, if the boat was on land it would not move. if you push off a big boat it will not move backwards because its mass is far greater than your body. so and even if it was floating on air it would still take more energy to overcome the inertia of the large vessel than it would take to overcome the inertia of your body, so basically its is two opposing forces, according to their mass.. by the way many people miss understand the meaning of inertia , it means" the force against an object which is standing still according to its mass",,,,, i have heard allot of people using the word to explain momentum which is wrong..... momentum is (,according to the velocity of an object, and its mass),, a force carrying the object forward until it stops

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Mass of the person = Mp      mass of boat = Mb
Initially both are at rest - let us say.  ( It does not matter even if the boat is moving with a uniform speed.)

Initial velocity of Person = Up  = 0    initial velocity of boat = Ub = 0
Final Velocity of P  = Vp           Final velocity of boat = Vb

Suppose the person jumps from the boat with a considerably velocity Vp in the forward direction.  Then let boat move by Vb velocity.

As conservation of momentum law says

   Mp Up + Mb Ub = Mp Vp + Mb Vb
   0 + 0  =  Mp Vp + Mb Vb
   Vb  =  - Mp Vp / Mb

So Vb is in the direction opposite to Vp.  It may be small, as Mb > Mp.
Even if it is a ship, When a person jumps off, the ship moves backwards, if we do not consider other external factors.  It may be a very small quantity.

It is the newtons third law that explains this phenomenon.  The person exerts a force F on the boat while jumping off, with his foot. So the boat moves backwards.  The force with which the man jumps, it comes from the normal reaction force F from the boat on the man. So both move in opposite directions with the force F given by the other.

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