Now that I've think about it more, even if we have the symmetric assumption (each person gets the same share), the pie share is not necessarily 1/n in that the utility of each person is different given a certain amount of pie.

for person 1 is not hungry at all, the pie is worth nothing to her and if she were to get 1/3 of the pie, she would not really even enjoy the consumption of it. Thus if person 1 were to get a tiny slice of pie, it could also be consider fair if we look at the symmetry in terms of utility instead of object. Well to achieve this, we can use a bidding system in which people bid for each infinitesimal part of the pie.

Either way, I believe that the argument that "each person gets 1/n of the pie is fair" is not sound because the worth of the pie is different for each person.