To slightly turn around FFF's explanation:
At high speeds the yaw & roll produced by an engine failure is very controllable due to the large aerodynamic forces that the control surfaces can produce. As speed reduces these forces also reduce. At some point in the speed reduction there will no longer be sufficient force able to be produced by the control surfaces to counteract the adverse effects caused by the engine failure. You've just reached Vmc
On the ground there is a beneficial effect to aid controllability from the forces produced by the wheels. Nosewheel steering, differential braking etc all supplement the control surface forces used to counteract the effects of the engine failure hence Vmcg (ground) is usually different to Vmca (air)
As for V1 not being less than Vmc: Speeds >V1 means 'continue the take off'. With a hypothetical engine failure at a V1<Vmc, would you really want to get airborne at a speed that is less than what you need to control the a/c?