Vmcg = minimum speed at which the aircraft can be controlled, on the ground, with full power on one engine, and the second engine inop.
V1 = the speed after which, if an engine failure occurs, you continue.
If V1 were less than Vmcg, and you had an engine failure at, or shortly after, V1, you would then have full power on one engine, and the second engine inop - at a speed which is lower than Vmcg, and therefore, by definition, the aircraft would not be controllable
It is generally fair to say that you do not want your aircraft to be in an uncontrollable state for very long
Therefore, you ensure that V1 is the same as, or higher than, Vmcg. This way, if an engine fails before Vmcg, it will also be before V1, and will therefore be followed by closing the throttles and braking - which is controllable.
FFF
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