Typically a utilitarian (or anyone for that matter) would argue that suffering is important. But perhaps we ask him why suffering is important. And they respond that suffering is important because people are important, i.e. suffering is bad for someone.
Say we ask him what makes people important. He would respond by saying people matter because they can suffer.
But this has gone full circle: suffering matters because people matter, and people matter because suffering matters.
So which comes first, people or suffering? When we talk of suffering, we are referring to a negative valenced emotional state of a sentient organism, or a kind of condition of an organism.
But surely someone would be a bit insulted if they were told that it is not them that is being valued but the experience itself that is being valued, as if suffering has been abstracted from the experiencer. But the only reason I can see as to why the experiencer themselves would be important is because they can suffer. It's the same circle.
Perhaps a way out would be to identify persons with their experiences in a bundle theory of sorts. So when we say we find suffering important, it means that we find a negative valenced experience, necessarily paired to a self-model, to be important. Like they cannot be separated, a person just is their emotional vista. Suffering is always suffering of a person; it is their suffering. Thus the feeling of ownership of a negative experience is bad.
Give me your thoughts.