This problem is that the goal of this method of measuring social welfare (as expanded by Arrow and Debreu, among others) was to make welfare economics a positive science, that is, one without any value judgement. One requirement for Pareto Optimality (PO) is that there are no interpersonal utility comparisons. What is an interpersonal utility comparison, you may ask? Well, it is that simple thing you learned when you were 7 years old: put yourself in someone else's shoes.
Every person has a theoretical utility function (sort of like a personal function of happiness), that when maximized, indicates that my demands have been met. Pareto Optimality is theoretically reached when all the aggregate utility functions have been maximized, but without any regard distribution of resources. This means, I could get all the resources and my brother get none. The assumption that we do not compare utility functions implies that I will not consider the welfare (or resources) of another person. That the comparison of my own welfare, sitting in my sunny room on my computer, is incomparable to a person in Haiti who struggles find enough to eat. The idea is that I will never care and that any government (or resource-sharing-decider) should not care about comparing utility.
Value judgements (my situation is better than yours) have been avoided, but what exactly does this positive science achieve? Policies that lack an ability to make the most obvious of comparisons are more unrealistic than informative.