Approximately 4% of white dwarf stars exhibit infrared excesses indicative of dusty debris disks. Such disks are thought to form via a two-step process: first, an inwardly scattered planetesimal crosses the tidal disruption limit (e.g., the Roche radius) of the white dwarf and disrupts into dust. Second, Poynting-Robertson drag circularizes the orbits of the dust, resulting in a dusty debris disk. However, the temperature distribution of white dwarfs hosting such dusty debris disks differs significantly from the white dwarf population as a whole, being found exclusively around white dwarfs with effective temperatures cooler than 27,000 K. This is all the more puzzling given that dusty debris disk formation should favor younger, hotter white dwarfs, which are more likely to host dynamically unstable systems of planets and asteroids. We find that these observed debris disk statistics are a natural result of the physical processes defining the circumstellar regions in which debris disks can form. Debris disks must initially form inside of the stellar Roche radius to form dust, yet be far enough from the star to avoid sublimation in the extreme near-star thermal environment. Unlike the static Roche radius, this “sublimation radius” recedes toward the white dwarf as the star cools. We find that young, hot white dwarfs have sublimation radii outside of the Roche radius, precluding any stable region for debris disk formation. However, the sublimation radius of debris disk materials (typically silicates) crosses inside of the Roche radius once the white dwarf has cooled to ~27,000 K, enabling a stable region for debris disk formation; this stable region continues to grow as the white dwarf cools and the sublimation radius recedes.