When the hunger artist is still insanely popular, the public chooses a group of men to keep watch over him to make sure that he doesn't sneak a bite of food while they aren't around. Ironically, most of these men happen to be butchers. As their occupation suggests, these men don't appreciate the finer points of the art of starvation.
The watchmen's refusal to believe that the hunger artist is really starving causes the artist sincere anguish. By not trusting the artist, though, they are refusing to believe the evidence of their own eyes. After all, this guy is stuck in a cage and he's getting skinnier and skinnier all the time. The watchmen seem to represent a certain side of human nature that clings to the ordinary and refuses to acknowledge the extraordinary.