That's because only the egg that Smoochum hatched from is a Special Egg that has an increased Shiny chance and the Pokemon learning Dizzy Punch.
Odd EggC: From the Day-Care Man. Will hatch into a Pichu, Cleffa, Igglybuff, Tyrogue, Smoochum, Elekid, or Magby that knows Dizzy Punch. It has a 14% chance of being Shiny in international versions. In the Japanese version of Crystal, the Day-Care Man instead gives out an Egg Ticket that can be traded in at the Pokémon Communication Center for the Odd Egg. The Odd Egg in the Japanese version has a 50% chance of being Shiny.