There seems to be a deep intuitive connection between morality and interpersonal trust: if you knew somebody to be morally perfect, then you would trust them to keep their promises, not steal your possessions, not harm or kill you in your sleep, etc. But note that if utilitarianism is true, then this connection breaks down: there may be enumerable situations in which promise-breaking, theft, or even physical violence (up to and including murder) could serve to maximize utility. So if utilitarianism is correct, then you cannot necessarily trust the morally perfect person not to do these things. This is deeply unintuitive: one should not need to "sleep with one eye open" around a morally perfect person.
Here's another way of thinking about this: suppose Joe finds himself stranded with a group of strangers on a desert island. If Joe finds out that these people are morally perfect, should he feel more safe, or less safe? If utilitarianism is true, then the answer is far from clear: after all, total utility might be maximized by their killing and eating Joe, or even by their exploiting him for pleasure (assuming their group is large enough for the total utility generated by their pleasure to outweigh his suffering). It would be more in Joe's interest for the group to be made up entirely of radical deontologists. But if utilitarianism is right, then this is surely backwards: Joe should not be hoping that his fellow island-refugees are seriously mistaken about fundamental morality.
One might object that in the vast majority of cases, the aforementioned behaviors will not contribute to the maximization of utility. But this depends on highly contingent sociological facts: for example, whether or not murdering me in my sleep to take my organs would maximize utility depends on whether there are friends to mourn my death, police to apprehend my killer, and so on. These don't seem like the sort of considerations that ought to motivate a morally perfect person not to slit my throat.
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