I know that this won't work but I'm asking Why?
Becuase as far as the vehicle POV - there is a force which drags him to the right.
Isnt $F=ma$ applies here? What is that im missing?
This is because how much ever force the magnet is applying on the IRON (not any metal) is opposed by an equal force applied by the iron on the magnet! And since the magnet is a part of the vehicle, this force will cancel out the force on iron by the magnet. Magnetic force occurs both ways!
Therefore, there is no NET force on the whole vehicle, which is why it won't move. What will happen is that the magnet and iron will be pulled to each other, and stick. If the rod connecting the vehicle to the magnet is rigid, and can withstand the magnetic force, nothing will happen.
You should remember internal forces never can produce a change in momentum of the system as a whole.
Another example is if you try to push a car while sitting in it. No doubt, the car will recieve a force pushing it in a direction, but that force will be canceled out by the force you are unknowingly applying on the car in the exact backward direction. This force is applied by your feet while stopping themselves from slipping: