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my aim is to show that Mass = Volume x height:
M = Vh Also, F = Ma
so, F = Ma = Vha
since Ma = Vha, M = Vh -- which is what I said before, so it must be true!
That line of thinking doesn't prove anything. The equation doesn't know what real life application it has, all the equation knows is whether the symbols are sticking to the rules of algebra, which they are. If we try and use this in real life, it will make no sense whatsoever; but that's why we derive the laws using other means -- not flawed algebraic manipulation.