Which point has zero potential between equally charged parallel plates? Or, can we say the mid point is zero potential?
The point where we choose the zero potential is arbitrary. However, not all points are clever choices. If you would like to determine potential due to point charges, infinity is a good choice.
When we deal with conducting parallel plates on the other hand , we can think of them as infinite conductors with uniform charge densities, given that the distance between the plates is small in comparison to the dimensions of plates. Then the electric field becomes uniform between the plates (though we cannot say so near the upmost and downmost parts). Choosing potential to be zero at infinity may not be a good choice this time because in the case of an infinite plane, potential would turn out to be infinite for every points in space. And of course we cannot speak of potential differences for this reason. Good choice is to choose negatively charged plate to be at zero potential and everything works just fine.