In my Schizophrenic Theory of Lost, I tried to provide a plausible explanation for "how" Dave might have manifested (i.e., Hurley's bicameral mind). In this update, I posit a simple explanation "why" I think Dave appeared to Hurley when he did on the Island.
Recall that Dave manifests shortly after Hurley has destroyed his stash of junk food. Upon doing so, Hurley tells Libby "I feel free!" They then stumble on the food drop, where Sawyer tries to renlist Hurley as food distributor. When Hurley refuses, Dave appears.
I believe the timing of that appearance was no coincidence. Someone (or thing) sensed that Hurley was beginning to break free of the Island's hold over his mind. When this suspicion was confirmed by Hurley's refusal to reassume food duty (Hurley's "job" as Locke once put it) Dave was sent as a probe.
Notice how Dave next appears when Hurley has broken down and is scarfing his deliciously salty Dharma snacks. Dave nods approvingly until Hurley drops the box and denies Dave's reality. When Dave next appears, it's to convince Hurley to kill himself.
I believe that was no coincidence, either. The Island was testing its psychic control over Hurley's mind. When he demonstrated disturbing signs of liberation, the Island decided to give him a scare.